Question

Find the values of x and y in the diagram.

Answer 1

Answer:

x = 15

y = 10

Step-by-step explanation:

ΔTUR is a 60°-60°-60° triangle because all angles are equal and  180/3 is 60

therefore, the angle adjacent to ∡R is 120 because it forms a straight line (which measures 180 degrees)

that means that angles T and S (which are both 3y°) plus angle R equal 180 so you can set up this equation to find y:  120 +6y = 180

                                                                6y = 60

                                                                 y = 10

Because angles T and S are the same we know that TR and TS are also the same, so RT is 15

ΔTUR is equiangular which means it is also equilateral; so if RT is 15 then UT and UR are 15 also

If UT = 15, we can write this equation: x - 5 = 15 and find that x = 20