# Question #be4d4

Feb 21, 2017

The reqd. Angles of the $\Delta \text{ are, } {70}^{\circ} , {30}^{\circ} , {80}^{\circ} .$

#### Explanation:

Let the Base Angle and Vertex Angle be, $B \mathmr{and} V ,$ resp.

By what is given, we get the following eqns. :

$\left(1\right) : V - B = 40 , \mathmr{and} , \left(2\right) : V + B = 100.$

$\therefore \left(1\right) + \left(2\right) \Rightarrow \left(V - B\right) + \left(V + B\right) = 40 + 100.$

$\therefore 2 V = 140 \Rightarrow V = \frac{140}{2} = 70.$

$\text{Then, from } \left(2\right) , 70 + B = 100 \Rightarrow B = 100 - 70 = 30.$

Finally, the remaining ${3}^{r d}$ Angle, is $180 - 70 - 30 = 80.$

Thus, the reqd. Angles of the $\Delta \text{ are, } {70}^{\circ} , {30}^{\circ} , {80}^{\circ} .$