Question

You know 3 angles, angle one at the top has an equation of (y+x)° angle two has the equation (y-x)° angle three at the bottom is blank and angle 4 at the left has the equation 2x° you need to figure out what each angle measures to. angle one at the top and angle four to the left are a linear pair, same with angle 1 and 2 at the right, and 2 and 4 are vertical angles and angles 1 and 3 are vertical angles angle 1 and 3 are obtuse while angle 2 and 4 are acute.

Answer 1

2x° = 2(30) = 60°

(y+x)° = 90° + 30° = 120°

(y-x)° = 90 - 30 = 60°

Explanation:

2x° and (y-x)° are vertical angles.

Vertical angles are equal.

equating both:

2x = y - x

2x+x = y

3x = y

Also 2x° + (y+x)° = 180° (angles on a straight line)

2x + x + y = 180

3x + y = 180°

recall, 3x = y

Insert the value of y in the equation: 3x + y = 180°

y + y = 180

2y = 180

y = 180/2

y = 90°

y = 3x

x = y/3 = 90/3

x = 30°

One of the angle: 2x° = 2(30) = 60°

(y+x)° = 90° + 30° = 120°

(y-x)° = 90 - 30 = 60°