Question

Find the values of x and y in the diagram. ​

Answer 1

Answers:

x = 18

y = 6

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Step-by-step explanation:

Focus on triangle TRS. This triangle has congruent base angles as shown by the double arcs. This means that the sides opposite these angles (TR and RS) are congruent. So TR = RS.

Because RS = 11, this makes TR = 11 too.

Now move onto triangle UTR. This triangle is equilateral because each angle is the same measure (each angle being 60 degrees).

So UT and TR are the same length, and,

UT = TR

x-7 = 11

x-7+7 = 11+7

x = 18

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Since every angle of triangle UTR is 60 degrees, this makes angle URT 60 degrees and angle TRS to be 180-60 = 120 degrees.

Move back to triangle TRS. We have these interior angles:

• R = 120
• T = 5y
• S = 5y

For any triangle, the interior angles always add to 180

R+T+S = 180

120+5y+5y = 180

10y+120 = 180

10y = 180-120

10y = 60

y = 60/10

y = 6