Question

$△$XYZ is constructed such that XY = 5 cm, XZ = 4 cm and $\angle$X = 25${}^{\circ }$. Then the difference between the lengths of sides YZ and XY is equal to

• A. 51${}^{\circ }$
• B. 53${}^{\circ }$
• C. 55${}^{\circ }$
• D. 57${}^{\circ }$

Answer 1

The correct option is B

53${}^{\circ }$

Step 1:
Draw the base line XY of the length 5 cm.

Step 2:
Measure the angle X with your protractor. Make a mark at 25 degrees and draw a line from X passing through the mark.

Step 3:
Cut an arc of radius 4 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 $\angle$Y = 51${}^{\circ }$ and $\angle$Z= 104${}^{\circ }$

Now, the difference between the measures of angle Z and that of angle Y is equal to 53${}^{\circ }$