Question

If $x={20}^{\circ }$ and $y={30}^{\circ }$ in the given figure, find the value of z.

• A. 60°
• B. 70°
• C. 80°
• D. 90°

Answer 1

The correct option is B

70°

Create the new line so that the given figure breaks into two triangles.

From our definitions, we know that every triangle will have interior angles that add up to ${180}^{\circ }$.

We also know that the two angles we created will be equal.

Remaining angle is ${180}^{\circ }-{30}^{\circ }–{20}^{\circ }-{20}^{\circ }={110}^{\circ }$

Now, we can divide that number in half to find the measurement of each of the two equal angles.

So, each angle is ${55}^{\circ }$.

Value of $Z={180}^{\circ }-({55}^{\circ }-{55}^{\circ })$

$={70}^{\circ }$