Question

Find the measure of Angle 1. measure of angle 1 = xmeasure of angle 2 = x-6

Answer 1

Answer:

The measure of ∠1 is 48°.

Step-by-step 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°

$x=\frac{92^o}{2}=48^o$

The measure of ∠1 is 48°.

Answer 2

Answer:

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.

Step-by-step 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.