Question

$△$ABC is constructed such that AB = 5 cm, AC = 6 cm and $\angle$B = 60${}^{\circ }$. Then, the sum of the measure of $\angle$B and $\angle$C is

• A. lies between 80${}^{\circ }$ and 90${}^{\circ }$
• B. lies between 90${}^{\circ }$ and 100${}^{\circ }$
• C. lies between 100${}^{\circ }$ and 110${}^{\circ }$
• D. lies between 110${}^{\circ }$ and 120${}^{\circ }$

Answer 1

The correct option is C lies between 100${}^{\circ }$ and 110${}^{\circ }$

Step 1:
Draw a line segment of AB of length 5 cm.

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

Step 3:
Draw an arc of radius 6 cm with centre at A.

Step 4:
Draw an arc to cut the line from B.

Step 5:
Mark the intersecting point as C.

Step 6:
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 41${}^{\circ }$.

Now, measure of angle B + measure of angle C = 67${}^{\circ }$ + 41${}^{\circ }$ = 108${}^{\circ }$