Answer:
Y = 6 and X = 18
Step-by-step explanation:
The triangle on the far left in a triangle with all angles of the same value. This means that all angles are equal to 60 degrees, and we can use this information to find the angles for the far right triangle!
For the far right triangle, angle R is shown to be of an unknown value plus the value of 60 according to how a straight line always equals 180 degrees. This means that 180 = x + 60, or 120 equals x. x is the assigned variable for angle R on the far right triangle only. For this reason, as the two lines on that far right triangle show that angle T and angle S are congruent, we take 180, minus 120 from the previously found angle to equal 60. As angle T and angle S are congruent, we can divide 60 by 2 to equal 30. This means that the far right triangle has angle T as 30, and we divide 30 by 5 to equal 6. This means that y is equal to 6. Now let's find the value of x!
As the far left triangle has all congruent angle measurements, we can say that each side of that triangle has equal side lengths. This means that every side of the far left triangle has a side length of x - 7. As the far right triangle is an isosceles triangle, the sides on both sides of angle R are the same. This means that the value of 11 on side RS is also the value of 11 on side RT. As the far left triangle also shares this side with the value of x - 7, we can make the equation x - 7 = 11. This means that x is equal to 18!
Therefore, the value of y is 6 and the value of x is 18!
