Question 1

Two lines intersect each other. One of the angles formed is 65°. What is the measure of the angle adjacent to it on a straight line?

Accepted Answer

Step 1: When two lines intersect, adjacent angles on a straight line are supplementary (they add up to 180°). Step 2: If one angle is 65°, then the adjacent angle = 180° − 65° = 115°. Therefore, the answer is 115°.

Question 2

Two lines intersect each other. If one of the angles formed at the intersection is 65°, what is the measure of its vertically opposite angle?

Accepted Answer

Step 1: Recall the Vertically Opposite Angles theorem — when two lines intersect, vertically opposite angles are always equal. Step 2: The angle vertically opposite to 65° is also 65°. Therefore, the answer is 65°.

Question 3

Two straight lines intersect each other. One of the angles formed is 35°. A third line is drawn parallel to one of the intersecting lines. If this third line intersects the second line, what is the measure of the acute angle between the third line and the second line?

Accepted Answer

Step 1: When two lines intersect, they form two pairs of vertically opposite angles. One angle is 35°, so the adjacent angle is 180° − 35° = 145°. Step 2: The second intersecting line makes angles of 35° and 145° with the first line. Step 3: When a third line is drawn parallel to the first line and intersects the second line, by the property of corresponding angles (or alternate angles), the angle between the third line and the second line equals one of the angles the second line makes with the first line. Step 4: The acute angle will be 35°.

Question 4

Two lines intersect each other. If one of the angles formed is 65°, what is the measure of the angle adjacent to it on a straight line?

Accepted Answer

Step 1: When two lines intersect, adjacent angles on a straight line are supplementary (sum to 180°). Step 2: If one angle is 65°, the adjacent angle = 180° - 65° = 115°. Therefore, the answer is 115°.

Question 5

An exterior angle of a triangle is 110°. If the two non-adjacent interior angles are in the ratio 3:2, what is the measure of the larger non-adjacent interior angle?

Accepted Answer

Step 1: By the exterior angle theorem, an exterior angle equals the sum of the two non-adjacent interior angles. Step 2: Let the non-adjacent interior angles be 3x and 2x. Step 3: 3x + 2x = 110°. Step 4: 5x = 110°, therefore x = 22°. Step 5: The larger angle = 3x = 3(22°) = 66°. Therefore, the answer is 66°.

Question 6

Two complementary angles are in the ratio 1:5. What is the measure of the smaller angle?

Accepted Answer

Step 1: Let the two complementary angles be x and 5x. Step 2: Complementary angles sum to 90°. So, x + 5x = 90°. Step 3: 6x = 90°, therefore x = 15°. Step 4: The smaller angle = x = 15°. Therefore, the answer is 15°.

Question 7

Three angles of a triangle are in the ratio 2:3:4. What is the measure of the largest angle?

Accepted Answer

Step 1: Let the three angles be 2x, 3x, and 4x. Step 2: Sum of angles in a triangle = 180°. So, 2x + 3x + 4x = 180°. Step 3: 9x = 180°, therefore x = 20°. Step 4: The largest angle = 4x = 4(20°) = 80°. Therefore, the answer is 80°.

Question 8

A transversal intersects two parallel lines. If one of the alternate interior angles is 72°, what is the measure of the other alternate interior angle?

Accepted Answer

Step 1: When a transversal intersects two parallel lines, alternate interior angles are equal. Step 2: If one alternate interior angle is 72°, the other alternate interior angle = 72°. Therefore, the answer is 72°.

Question 9

A line makes an angle of 35° with the horizontal. What is the angle it makes with the vertical?

Accepted Answer

Step 1: Horizontal and vertical lines are perpendicular to each other, forming a 90° angle. Step 2: If a line makes 35° with the horizontal, it makes 90° − 35° = 55° with the vertical. Therefore, the answer is 55°.

Question 10

Two lines intersect each other. One of the angles formed is 65°. What is the measure of the angle adjacent to it on a straight line?

Accepted Answer

Step 1: When two lines intersect, adjacent angles on a straight line are supplementary (they add up to 180°). Step 2: If one angle is 65°, then the adjacent angle = 180° − 65° = 115°. Therefore, the answer is 115°.

Question 11

A line makes an angle of 35° with the horizontal. What is the angle it makes with the vertical?

Accepted Answer

Step 1: The horizontal and vertical lines are perpendicular to each other, forming a 90° angle. Step 2: If a line makes 35° with the horizontal, the angle with the vertical = 90° - 35° = 55°. Therefore, the answer is 55°.

Question 12

Two parallel lines are cut by a transversal. If one of the alternate interior angles is 72°, what is the measure of the corresponding angle on the same side of the transversal?

Accepted Answer

Step 1: When a transversal cuts two parallel lines, alternate interior angles are equal. Step 2: If one alternate interior angle is 72°, the other alternate interior angle is also 72°. Step 3: Corresponding angles are also equal when lines are parallel. Step 4: The corresponding angle on the same side = 72°. Therefore, the answer is 72°.

Question 13

At an intersection of two straight lines, one angle is 4 times another angle. What is the measure of the smaller angle?

Accepted Answer

Step 1: When two straight lines intersect, adjacent angles are supplementary (sum to 180°). Step 2: Let the smaller angle be x and the larger angle be 4x. Step 3: x + 4x = 180°, so 5x = 180°, thus x = 36°. Step 4: The smaller angle = 36°. Therefore, the answer is 36°.

Question 14

Two lines intersect each other. If one of the angles formed is 65°, what is the measure of the angle adjacent to it on a straight line?

Accepted Answer

Step 1: When two lines intersect, adjacent angles on a straight line are supplementary (sum to 180°). Step 2: If one angle is 65°, the adjacent angle = 180° - 65° = 115°. Therefore, the answer is 115°.

Question 15

Two parallel lines are cut by a transversal. If one of the alternate interior angles is 72°, what is the other alternate interior angle?

Accepted Answer

Step 1: When a transversal cuts two parallel lines, alternate interior angles are equal. Step 2: If one alternate interior angle is 72°, the other alternate interior angle is also 72°. Therefore, the answer is 72°.

Question 16

Two complementary angles are in the ratio 1:5. What is the measure of the smaller angle?

Accepted Answer

Step 1: Complementary angles sum to 90°. Step 2: Let the angles be x and 5x. Step 3: x + 5x = 90°, so 6x = 90°, thus x = 15°. Step 4: The smaller angle = x = 15°. Therefore, the answer is 15°.

Question 17

If two supplementary angles are in the ratio 4:5, what is the measure of the larger angle?

Accepted Answer

Step 1: Let the two supplementary angles be 4x and 5x. Step 2: Supplementary angles sum to 180°. So, 4x + 5x = 180°. Step 3: 9x = 180°, therefore x = 20°. Step 4: The larger angle = 5x = 5(20°) = 100°. Therefore, the answer is 100°.

Question 18

A transversal intersects two parallel lines. If one of the alternate interior angles is 72°, what is the measure of the other alternate interior angle?

Accepted Answer

Step 1: When a transversal intersects two parallel lines, alternate interior angles are equal. Step 2: If one alternate interior angle is 72°, the other alternate interior angle is also 72°. Therefore, the answer is 72°.

Question 19

Three lines meet at a point. The angles formed are in the ratio 2:3:4. What is the measure of the largest angle?

Accepted Answer

Step 1: When three lines meet at a point, the sum of all angles around that point is 360°. Step 2: Let the angles be 2x, 3x, and 4x. Step 3: 2x + 3x + 4x = 360°, so 9x = 360°, thus x = 40°. Step 4: The largest angle = 4x = 4(40°) = 160°. Therefore, the answer is 160°.

Question 20

Two lines intersect such that one of the angles formed is 65°. If a third line is drawn parallel to one of the original lines and passes through the point of intersection, what is the measure of the acute angle between this third line and the second original line?

Accepted Answer

Step 1: When two lines intersect, they form four angles. One angle is 65°, so the adjacent angle is 180° − 65° = 115°. Step 2: When a third line is drawn parallel to the first line through the intersection point, by the property of parallel lines and transversals, the angle between the third line and the second line equals the angle between the first and second lines. Step 3: The acute angle between the original two lines is 65°. Therefore, the acute angle between the third line and the second line is also 65°.

Question 21

A transversal intersects two lines. The co-interior angles (same-side interior angles) are (2x + 10)° and (4x − 40)°. If the lines are parallel, what is the measure of the smaller co-interior angle?

Accepted Answer

Step 1: Co-interior angles formed by a transversal cutting parallel lines are supplementary (sum to 180°). Step 2: (2x + 10) + (4x − 40) = 180. Step 3: 6x − 30 = 180. Step 4: 6x = 210, so x = 35. Step 5: First angle = 2(35) + 10 = 80°. Step 6: Second angle = 4(35) − 40 = 100°. Step 7: The smaller angle is 80°.

Question 22

In a triangle, one exterior angle is 120°. The two non-adjacent interior angles are in the ratio 3:5. What is the measure of the larger non-adjacent interior angle?

Accepted Answer

Step 1: By the exterior angle theorem, an exterior angle equals the sum of the two non-adjacent interior angles. Step 2: Therefore, the sum of the two non-adjacent interior angles = 120°. Step 3: Let the angles be 3x and 5x. Step 4: 3x + 5x = 120°. Step 5: 8x = 120°, so x = 15°. Step 6: The larger angle = 5x = 5 × 15° = 75°.

Question 23

In a triangle, one angle measures 48° and another measures 67°. What is the measure of the third angle?

Accepted Answer

Step 1: The sum of all angles in a triangle is 180°. Step 2: Third angle = 180° - 48° - 67° = 180° - 115° = 65°. Therefore, the answer is 65°.

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