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.
To find the value of x, we can set up an equation using the information given.
From the given, we know that angle SRT = 20 degrees and angle STU = 4x. Since angle SRT is congruent to angle STR, we can also say that angle STR = 20 degrees.
Now, we can use the fact that the sum of angles in a triangle is 180 degrees:
angle SRT + angle STR + angle STU = 180
Substituting the values we have:
20 + 20 + 4x = 180
Simplifying the equation:
40 + 4x = 180
Subtracting 40 from both sides:
4x = 140
Dividing both sides by 4:
x = 35
So, the value of x is 35.