Question

Given the information depicted in the diagram below, find the measure of ∠S. Describe how you arrived at your answer. Be sure to write a complete sentence for each sub-step of your solution. In your written response, include the key vocabulary terms” isosceles triangle”, “vertical angles”, and “congruent”.

Answer 1

Answer is 44

Explanation:

I'll do some of it. You can supply some of the vocabulary.

<Q = 56 degrees The triangle is isosceles.

<PRQ = 180 - 56 - 56 All triangles have 180 degrees.

<PRQ = 68 Do the subtraction

<PRQ = <SRT Why is this so? You have the term.

<TRS = 68 degrees The reason is the same as the last part.

<T = <RST The triangle is isosceles (2 equal angles)

<T = 68 Two equal angles = the same degrees

S = 180 - <T - < RST S is the left over from the 2 equal angles.

S = 180 - 68 + 68 Substitute.

S = 44

Answer 2

Answer 44

Explanation:

I'll do some of it. You can supply some of the vocabulary.

<Q = 56 degrees The triangle is isosceles.

<PRQ = 180 - 56 - 56 All triangles have 180 degrees.

<PRQ = 68 Do the subtraction

<PRQ = <SRT Why is this so? You have the term.

<TRS = 68 degrees The reason is the same as the last part.

<T = <RST The triangle is isosceles (2 equal angles)

<T = 68 Two equal angles = the same degrees

S = 180 - <T - < RST S is the left over from the 2 equal angles.

S = 180 - 68 + 68 Substitute.

S = 44