Question
In the figure above, RT = TU. What is the value of x?
- 72
- 66
- 64
- 58
Hint:
In geometry, an isosceles triangle is a triangle that has two sides of equal length. Hence, the two angles opposite to the equal sides are congruent (or, equal) to each other. In the given diagram, ΔABC is a isosceles triangle, with (A ̅B) = (A ̅B) and ∠B = ∠C.
The correct answers are: 72, 64
Step 1 of 3:
In the given figure, RT = TU. So, ΔTRU is a isosceles triangle and hence, ∠TRU=∠TUR.
Given, ∠RTU = 114°.
Now, in triangle TRU,
∠RTU + ∠TRU + ∠TUR=180 (Since, in a Euclidean space, the sum of angles of a triangle equals the straight angle, 180°)
⇒114 + 2 ×∠TUR=180
⇒ 2 × ∠TUR = 180 – 114 = 66
⇒ ∠TUR = 
= 33
Step 2 of 3:
Given, ∠VSU = 31° and we have ∠TUR = ∠SUV = 33°.
Now, in triangle SUV, ∠SVU + ∠SUV + ∠VSU = 180
⇒ ∠SVU + 33 + 31 = 180
⇒ ∠SVU = 180 - (33 + 31) =180 - 64 = 116
Step 3 of 3:
Now, ∠SVR and ∠SVU are linear pair. So, ∠SVR + ∠SVU = 180
⇒ ∠SVR + 116 = 180
⇒ ∠SVR = 180 -116 = 64
Therefore, ∠SVR = x = 64°.
Final Answer:
The value of x is— C) 64.
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