Question

Geometry question

What are the numerical measures of each angle in the diagram?

∠1 and ∠3 ____ degrees

∠2 and ∠4 ____ degrees

Answer 1

1. The measure of angle 1 and 3 is 29°

2. The measure of angle 2 and 4 is 151°

Vertical angles are pairs of angles formed by intersecting lines or rays.

They are opposite each other and have equal measures. Vertical angles share a common vertex but have no common sides, forming an "X" shape.

Angle 1 = angle 3( vertically opposite angles)

angle 2 = angle 4 ( vertically opposite angles)

2x + 9 = 3x - 1

2x - 3x = -1 - 9

-x = -10

x = 10

Therefore angle 3 = 2(10) + 9 = 29°

angle 2 = 180 - 29 = 151°

angle 3 = angle 1 = 29°

angle 2 = angle 4 = 151°