Question

Need to know the following angle

Answer 1

Given:

$m\angle A=(2x-15)^\circ$

$m\angle B=(x-5)^\circ$

$\text{Exterior}\ m\angle C=148^\circ$

To find:

The $m\angle ABC$.

Solution:

In triangle ABC,

$\text{Exterior}\ m\angle C=m\angle A+m\angle B$          [Exterior angle theorem]

$148=(2x-15)+(x-5)$

$148=3x-20$

$148+20=3x$

$168=3x$

Divide both sides by 3.

$\dfrac{168}{3}=x$

$56=x$

Now,

$m\angle ABC=(x-5)^\circ$

$m\angle ABC=(56-5)^\circ$

$m\angle ABC=51^\circ$

Therefore, $m\angle ABC=51^\circ$.