We want to find the measure of ∠1. To do so, recall that according to the Exterior Angle Theorem, the measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Let's write an equation applying this theorem.
5x-10=40+3xWe will now solve the above equation for x.
Now we can substitute x= 25 into the expression 3x to find the measure of this angle.
3( 25)=75
The Triangle Angle-Sum Theorem states that the measures of the interior angles of a triangle add up to 180. Therefore, knowing that the measures of two of the interior angles are 40 and 75, we can write an equation to find m∠1.
40+75+ m∠1=180
We can find the measure of ∠1 by solving this equation. Let's do it!
