Question

what is the value of y in the given figure below? a (x)° e 35° 75° 77° (y)° c b o a. y = 70 o b. y = 75 o c. y = 80 o d. y = 65

Explanation:

Step1: Find angle AEC's supplementary angle

$\angle AEC = 75^{\circ}$, and $\angle BED=\angle AEC = 75^{\circ}$ (vertically - opposite angles are equal).

Step2: Use angle - sum property of a triangle

In $\triangle BDE$, we know that the sum of interior angles of a triangle is $180^{\circ}$. Let $\angle D = 35^{\circ}$, $\angle BED=75^{\circ}$, and $\angle B=y$. Then $y + 35^{\circ}+75^{\circ}=180^{\circ}$.
So, $y=180^{\circ}-(35^{\circ} + 75^{\circ})$.
$y = 70^{\circ}$.

Answer:

A. $y = 70$