Question

$A,B,C$ are the three angles of a triangle . if $A-B=$${15}^{\circ }$ , $B-C=$${30}^{\circ }$ , find $\angle A$ , $\angle B$ ,$\angle C$.

Answer 1

We have,

$A-B={15}^{\circ }$ ......(1)

$B-C={30}^{\circ }$

$B=C+{30}^{\circ }$ ......(2)

On adding both equation, we get

$A-C={45}^{\circ }$

$A=C+{45}^{\circ }$ ......(3)

In a triangle,

$A+B+C={180}^{\circ }$ ......(4)

Substituting the value from equation (1) and (2), we get

$C+{45}^{\circ }+C+{30}^{\circ }+C={180}^{\circ }$

$3C={105}^{\circ }$

$\angle C={35}^{\circ }.$

Substituting this value in equation (1) and (2), we get

$\angle B={65}^{\circ }$

$\angle A={80}^{\circ }$

Hence, the angles are $\angle A={80}^{\circ }$ $\angle B={65}^{\circ }$ $\angle C={35}^{\circ }.$