Question

Find the measure of each numbered angle and name the theorem that justifies your work.

m∠11 = 11x
m∠13 = 10x + 12

a) m∠11 = 66°, m∠13 = 62°, Theorem = Vertical Angles Theorem
b) m∠11 = 11°, m∠13 = 10°, Theorem = Corresponding Angles Theorem
c) m∠11 = 55°, m∠13 = 52°, Theorem = Alternate Interior Angles Theorem
d) m∠11 = 110°, m∠13 = 102°, Theorem = Linear Pair Theorem

Answer 1

To find the measure of each numbered angle, we can use the fact that vertical angles are congruent and corresponding angles are congruent. By setting up equations and solving for the variable, we can find the measures of the angles. In this case, each numbered angle is 132°, and the Corresponding Angles Theorem justifies our work.

Step-by-step explanation:

To find the measure of each numbered angle, we need to set up an equation using the given information. We can use the fact that vertical angles are congruent and corresponding angles are congruent. So, we have:

m∠11 = m∠13 = 11x = 10x + 12

Solving this equation, we get:

x = 12

Substituting this value back into the equations, we get:

m∠11 = 11(12) = 132°

m∠13 = 10(12) + 12 = 132°

Therefore, the measure of each numbered angle is 132° and the theorem that justifies our work is the Corresponding Angles Theorem.