Question

Part A

3. Which theorems or postulates allow you to find the value of y?

[] Vertical Angles Theorem and Triangle Angle-Sum Theorem
[] Triangle Exterior Angles Theorem and Vertical Angles Theorem
[] Triangle Angle-Sum Theorem and Angle Addition Postulate
[] Angle Addition Postulate and Triangle Exterior Angles Theorem


Part B
3. Find the value of each variable.

[] x = 80, y = 100
[] x = 80, y = 80
[] x = 100, y = 80
[] x = 100, y = 100

Answer 1

x=80 and y=80

Explanation:

70° + 30° + x = 180°

100° + x = 180°

-100 -100

x= 80°.

Angles x and y are vertical, then they are congruent.

Answer 2

Definition: Vertical angles are the angles that are vertically opposite to each other when two lines intersect.

Vertical Angles Theorem: Vertical angles are congruent to each other.

Triangle Angle-Sum Theorem: The sum of the measures of the interior angles of a triangle is 180°.

The diagram shows triangle with to given angles. By the Triangle Angle-Sum Theorem you can find the measure of third angle. Angles x and y are vertical, then they are congruent.

Answer Part A: option A

By the Triangle Angle-Sum Theorem, x°+30°+70°=180°,

x°=80°

and

x°=y°=80°.

Answer part B: option B