Answers:
x = 20
y = 10
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Explanation:
Note the angles of triangle URT are all the same due to the similar arc markings. Each angle of this triangle is 60 degrees because 60+60+60 = 180.
Since angle URT is 60 degrees, this makes angle TRS to be 180-60 = 120 degrees. Angles URT and TRS are supplementary, meaning they add to a straight angle of 180 degrees.
Focus on triangle TRS. We have the top angle equal to 120 we found earlier. The two bottom base angles are both equal to 3y. We know they're equal because of the arc markings they share.
Triangle TRS has the angles of 120, 3y and 3y. Add these angles up, set the sum equal to 180 and solve for y
120+3y+3y = 180
120+6y = 180
6y = 180-120
6y = 60
y = 60/6
y = 10
So that takes care of the value of y.
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Now to find the value of x.
Triangle TRS is isosceles because of the congruent base angles. The sides opposite these congruent base angles are side TR and side RS. We can say TR = RS for short.
Because RS = 15, we know that TR = 15 as well
Now move to triangle URT. This is an equilateral triangle. All equilateral triangles have interior angles of 60 degrees each.
By definition of what it means to be equilateral, we know that UT = TR
So UT = 15
Let's solve for x
UT = 15
x-5 = 15
x = 15+5
x = 20