Answer:
The actual measure of ∠1 = 40°
Step-by-step 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
[tex]2x+6+8x+4=180\\10x+10=180\\10x=180-10\\10x=170\\x=170/10\\x=17[/tex]
So, value of x = 17
Now, finding actual measure of ∠1 by putting x=17 in equation 2x+6
[tex]\angle1=2(17)+6\\\angle1=34+6\\\angle1=40[/tex]
So, the actual measure of ∠1 = 40°
