Question

As a part of her maths homework, Sharon has to identify the angles x, y, and z. If she already knows that z = 30°, help her find the the value of the angles x and y using the given triangle and parallelogram.

• A. x = y = 60°
• B. x = y = 75°
• C. x = 45°; y = 90°
• D. x = 80°; y = 70°

Answer 1

The correct option is B x = y = 75°

Studying the triangle, we find:

$Sumoftheinterioranglesofatriangle=180°$

$⟹x+y+z=180°$

$z=30°......\left(Given\right)$

$⟹x+y+30°=180°$
$⟹x+y=150°.......Equation1$

Now, studying the parallelogram, we find:

$Oppositeanglesinaparallelogramareequalinmeasure.$

$⟹x=y......Equation2$

From equations 1 and 2, we get:

$x+x=y+y=150°$
$⟹2x=2y=150°$
$⟹x=y=75°$