Short Answer
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)
The value of x is 5.
To find the value of x, we can use the information given:
1. We are given that angle SRT is congruent to angle STR. This means that angle SRT = angle STR.
2. We are also given that mangleSRT = 20.
3. Finally, we are given that mangleSTU = 4x.
Using these three pieces of information, we can set up an equation:
mangleSRT + mangleSTR + mangleSTU = 180 (sum of angles in a triangle)
Substitute the given values:
20 + 20 + 4x = 180
Combine like terms:
40 + 4x = 180
Subtract 40 from both sides:
4x = 140
Divide both sides by 4:
x = 35
Therefore, the value of x is 35.