We want to find the value of x and the measure of the labeled angles. Let's take a look at the given diagram. Notice that the labeled angles are vertical angles.
Therefore, by the Vertical Angles Theorem, they are congruent. This means that their measures are equal. From the given diagram, we know that the measure of one angle is given by the expression x+10 and the measure of the other angle is given by the expression 4x-35.
x+10 = 4x-35
Let's solve this equation for x.
We already know that the measures of both angles are equal. Therefore, both angles have a measure of 25 ^(∘).
Checking Our Answer
The Measure of the Other Angle
We found that x=15 and we substituted it into the expression x+10. We got that this angle measures 25 ^(∘) and because we knew that the measures of both angles are equal, we concluded that the measure of the other angle is also 25 ^(∘). Let's substitute x=15 into the expression 4x-35 to check it.
Substituting x=15 into the expression for the other angle measure also gives us that the measure of this angle is 25 ^(∘). Therefore, our solution is correct.
