1. part a which theorems or postulates allow you to find the value of y? a) vertical angles theorem and triangle angle-sum theorem  b) triangle exterior angles theorem and vertical angles theorem  c) triangles angle-sum theorem and angles addition postulate  d) angles addition postulate and triangles exterior angles theorem part b find the value of each variable a) x=80, y=100 b) x=80, y=80 c) x=100, y=80 d) x=100, y=100 2. find m< 1 a) 57 b) 63 c) 117 d) 123 3. which theorems or postulates could you use to find the measure of angle 1 in the previous question? (2 points) (2 answers) same-side interior angles theorem vertical angles theorem triangle angle-sum theorem triangle exterior angle theorem alternate exterior angles theorem 4. find the value of x a) x=5 b) x=13 c) x=37 d) x=73

The correct answer for Number 1 is

A.



First we apply the vertical angles theorem to transfer x into the triangle. That is,



Next, we use the triangle angle sum theorem to write an equation in x, which is



We can solve this equation for x.

Part B

We now solve the equation to obtain,





This gives us,



and



The correct answer for this part is B.

2)

By the triangle exterior angle theorem,



The correct answer for this part is D.

3) The correct answer is the Triangle exterior angle theorem.

This theorem says that the sum of any two adjacent interior angles of a triangle equals the exterior angle opposite to them.

4) Using the triangle angle sum theorem, we can solve for x.

So we are adding all the angles in the triangle and equate them to 180.



We group like terms to obtain,



This simplifies to,



we divide both sides by 5 to get,



The correct answer for this question 4 is C