Question

If measure of angle 1 = 2x+6 and measure of angle 2 = 8x+4 where angles 1 and 2 are supplementary, then how much is the actual measure of angle 1?\

Answer 1

The actual measure of ∠1 = 40°

Explanation:

We are given: ∠1 = 2x+6 and ∠2 = 8x+4

and both angles are supplementary. we need to find the actual measure of ∠1

Supplementary angles: If the angles are supplementary their sum is equal to 180°

In our case ∠1 +∠2 = 180°

2x+6+8x+4=180

Solving the equation to find x, then we can find the actual measure of ∠1

`2x+6+8x+4=180\\10x+10=180\\10x=180-10\\10x=170\\x=170/10\\x=17`

So, value of x = 17

Now, finding actual measure of ∠1 by putting x=17 in equation 2x+6

`\angle1=2(17)+6\\\angle1=34+6\\\angle1=40`

So, the actual measure of ∠1 = 40°