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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