Question

I need help
measure of each labeled angle

Answer 1

`\sf m\angle A = 3x - 20^o = \bf 100^o`

`\sf m\angle B = 2x = \bf 80^o`

`\sf m\angle C = 2x - 15^o = \bf 65^o`

Explanation:

A figure is given to us , in which two lines are parallel to each other. There are two transversals to the || lines . We know that the measure of a straight line is 180° . Therefore ,

`\sf\longrightarrow \angle A +\angle B = 180^o`

Substitute the given values ,

`\sf\longrightarrow 3x - 20^o + 2x = 180^o`

Simplify the RHS by adding the variables ,

`\sf\longrightarrow 5x - 20^o = 180^o`

Add 20° to both sides ,

`\sf\longrightarrow 5x = 180^o + 20^o`

Add the numbers in RHS ,

`\sf\longrightarrow 5x = 200^o`

Divide both sides by 5 ,

`\sf\longrightarrow \boxed{\blue{\sf x = 40^o}}`

Therefore ,

• 
  `\sf m\angle A = 3x - 20^o = \bf 100^o`

• 
  `\sf m\angle B = 2x = \bf 80^o`

• 
  `\sf m\angle C = 2x - 15^o = \bf 65^o`