Question

question 1 of 10
what is the value of y?
114°
a. 66°
b. 114°
c. 57°
d. 33°

Explanation:

Step1: Find adjacent interior angle

Use the linear - pair relationship. If an exterior angle of a triangle is \(114^{\circ}\), then the adjacent interior angle \(x\) satisfies \(x + 114^{\circ}=180^{\circ}\). So, \(x = 180^{\circ}-114^{\circ}=66^{\circ}\).

Step2: Use triangle - angle sum property

The sum of angles in a triangle is \(180^{\circ}\). Let the two equal angles be \(y\). We know one angle is \(66^{\circ}\), so \(y + y+66^{\circ}=180^{\circ}\). Simplify the equation: \(2y=180^{\circ}-66^{\circ}\), then \(2y = 114^{\circ}\).

Step3: Solve for \(y\)

Divide both sides of \(2y = 114^{\circ}\) by \(2\). So, \(y=\frac{114^{\circ}}{2}=57^{\circ}\).

Answer:

C. \(57^{\circ}\)