Note: Your teacher will grade your responses to questions 4–8 to ensure you receive proper credit for your answers.

Question

Find the value of x. The diagram is not to scale.

Given: angle upper S upper R upper T congruent to angle upper S upper T upper R, mangleSRT = 20, mangleSTU = 4x

Triangle upper R upper S upper T is shown with upper R in the lower left corner moving clockwise around to the other vertices. Segment upper R upper T is horizontal. Point upper U is drawn to the right of point upper T so that ray upper R upper U is formed and drawn.
(1 point)

Answer 1

We are given that angle RST is congruent to angle STR. This means that angle RST = angle STR.

We are also given that angle SRT = 20.

Since the sum of the angles in a triangle is 180 degrees, we can add up the three angles in triangle STR:

angle STR + angle SRT + angle STU = 180

Since angle SRT and angle STU are congruent and angle STR is 20, we can write:

angle STR + 20 + angle STU = 180

Now we can substitute 4x for angle STU:

20 + 4x = 180

Subtract 20 from both sides of the equation:

4x = 160

Divide both sides by 4:

x = 40

Therefore, the value of x is 40.