Question

Question 6
Write True or False and give reasons for your answer:

A $\Delta ABC$ can be constructed in which $\angle B={60}^{\circ },\angle C={45}^{\circ }$ and AB + BC + CA = 12cm.

Answer 1

True

We know that, sum of angles of a triangle is ${180}^{\circ }$.
$\therefore \angle A+\angle B+\angle C={180}^{\circ }$
$Here,\angle B+\angle C={60}^{\circ }+{45}^{\circ }={105}^{\circ }<{180}^{\circ }$
Thus, $\Delta ABC$ with given conditions can be constructed.