Question

Find the measure of Angle 1.

measure of angle 1 = x

measure of angle 2 = x-6

Answer 1

Angle 1 has degree measurement 48.

Angle 2 has degree measurement 42.

Angle 3 has degree measurement 90 because of the little square there in that spot of angle 3.

Explanation:

The measures of angles 1, 2 , and 3 add up to be 180 degrees because they share a common vertex laying on the line given.

Angle 3 has measurement of 90 degrees so this means angle 1 and 2 add up to be 90 degrees.

We are given the measurement of angle 1 and 2:

angle 1+ angle 2= 90

(x) + (x-6) = 90

x + x-6 = 90

Add like terms:

2x -6 = 90

Add 6 on both sides:

2x = 90+6

Simplify right hand side:

2x = 96

Divide both sides by 2:

x = 96/2

Simplify right hand side:

x = 48

x is 48 degrees.

x-6 is 48-6=42 degrees.

Angle 1 has degree measurement 48.

Angle 2 has degree measurement 42.

Answer 2

The measure of ∠1 is 48°.

Explanation:

Given : ∠1 = x , ∠2 = x-6, ∠3 = 90°

To find = ∠1

Solution:

∠1 + ∠2 + ∠3 = 180° ( Supplementary angle)

x + (x-6) + 90° = 180°

2x + 84° = 180°

2x = 180° - 84°

2x = 96°

`x=(92^o)/(2)=48^o`

The measure of ∠1 is 48°.