Question

$△$ABC is constructed such that AB = 3 cm, AC = 5 cm and $\angle$B = 67${}^{\circ }$. Then, the difference between the measure of $\angle$B and $\angle$C is

• A. lies between 5${}^{\circ }$ and 10${}^{\circ }$
• B. lies between 10${}^{\circ }$ and 20${}^{\circ }$
• C. lies between 20${}^{\circ }$ and 30${}^{\circ }$
• D. lies between 30${}^{\circ }$ and 40${}^{\circ }$

Answer 1

The correct option is B lies between 10${}^{\circ }$ and 20${}^{\circ }$

Step 1:
Draw a line segment of AB of length 3 cm.

Step 2:
Mark a ray making an angle 60${}^{\circ }$ at B.

Step 3:
Draw an arc of radius 5 cm with centre at A.

Step 4:
Mark the intersecting point as C.

Step 5:
Join CA to get the required $△$ABC



From the above construction, we see that the measure of angle B is 67${}^{\circ }$ and measure of angle C is 53${}^{\circ }$.

Now, measure of angle B - measure of angle C = 67${}^{\circ }$ - 53${}^{\circ }$ = 14${}^{\circ }$