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