Question

$△$XYZ is constructed such that XY = 4 cm, XZ = 8 cm and $\angle$X = 20${}^{\circ }$. Then, the sum of measures of $\angle$Y and $\angle$X is equal to _____.

• A. 38${}^{\circ }$
• B. 162${}^{\circ }$
• C. 160${}^{\circ }$
• D. 142${}^{\circ }$

Answer 1

The correct option is B

162${}^{\circ }$

Step 1:
Draw the base line XY of the length 4 cm.

Step 2:
Measure the angle X with your protractor. Make a mark at 20 degrees and draw a line from X passing through the mark.

Step 3:
Cut an arc of radius 8 cm on the line passing through the point X. The point where this arc cuts the line is the point Z.

Step 4:
Draw a line from Y to point Z to get the required triangle XYZ, as shown below.

From the above construction, we see that the measure of $\angle$Y is 142${}^{\circ }$.

Now,
$\angle$X + $\angle$Y = 20${}^{\circ }$ + 142${}^{\circ }$ = 162${}^{\circ }$