Question

If $\angle BAD$ and $\angle DAC$ form a linear pair and $a^{\circ }-b^{\circ }={60}^{\circ }$ then find the values of $a$ and $b$

Answer 1

$\angle BAD$ and $\angle DAC$ form a linear pair.

$\angle BAD+\angle DAC={180}^{\circ }$

$\Rightarrow a^{\circ }+b^{\circ }={180}^{\circ }$ .......$\left(1\right)$

Given:$a^{\circ }-b^{\circ }={60}^{\circ }$ ......$\left(2\right)$

Adding $\left(1\right)$ and $\left(2\right)$ we get

$2a^{\circ }={180}^{\circ }+{60}^{\circ }={240}^{\circ }$

$\Rightarrow a^{\circ }=\frac{{240}^{\circ }}{2}={120}^{\circ }$

Substitute $a^{\circ }={120}^{\circ }$ in $\left(1\right)$ we get

$b^{\circ }={180}^{\circ }-a^{\circ }={180}^{\circ }-{120}^{\circ }={60}^{\circ }$

$\therefore a={120}^{\circ }$ and $b={60}^{\circ }$