Question

question 7 of 10
what is the value of y?
a. 57°
b. 114°
c. 33°
d. 66°

Explanation:

Step1: Find the adjacent interior angle

Use the property that an exterior angle and its adjacent interior angle are supplementary.
Let the adjacent interior angle be \(x\). Then \(x + 114^{\circ}=180^{\circ}\), so \(x = 180^{\circ}- 114^{\circ}=66^{\circ}\).

Step2: Use the triangle - angle sum property

In a triangle, the sum of interior angles is \(180^{\circ}\). Let the angles of the triangle be \(x\), \(y\), and \(y\) (since two angles are \(y\)).
We know \(x + y + y=180^{\circ}\). Substitute \(x = 66^{\circ}\) into the equation: \(66^{\circ}+2y = 180^{\circ}\).
First, subtract \(66^{\circ}\) from both sides: \(2y=180^{\circ}-66^{\circ}=114^{\circ}\).
Then divide both sides by 2: \(y=\frac{114^{\circ}}{2}=57^{\circ}\).

Answer:

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