Question

88 1

2
3
81°
4
5
64%
m/1 =
m/2 =
m23 =
m/4 =
m25 =

Answer 1

1. 92°
2. 24°
3. 64°
4. 35°
5. 81°

Explanation:

You want the measures of 5 marked angles in the figure showing two transversals crossing parallel lines.

Angle 1

Angle 1 forms a linear pair with the angle marked 88°, so is supplementary to it.

Angle 1 = 180° -88°

Angle 1 = 92°

Angle 3

Angle 3 is a corresponding angle to the one marked 64° where the horizontal transversal crosses the parallel lines. Corresponding angles are congruent.

Angle 3 = 64°

Angle 2

Angles 2 and 3 are "remote interior angles" with respect to the exterior angle marked 88°. Hence their sum is 88°.

Angle 2 = 88° -Angle 3 = 88° -64°

Angle 2 = 24°

Angle 4

Angles 3, 4, and 81° combine to form a straight angle of 180°.

Angle 4 = 180° -64° -81°

Angle 4 = 35°

Angle 5

Angle 5 is an alternate interior angle with respect to the one marked 81° where the downward-sloping transversal crosses the parallel lines. Alternate interior angles are congruent.

Angle 5 = 81°