Question

Two angles measure $({55}^{\circ }+3a)$ and $({115}^{\circ }-2a)\cdot$ If each is supplement of the other, then calculate the value of $a.$

Answer 1

Given $({55}^{\circ }+3a),({115}^{\circ }-2a)$ are supplementary angles

$⟹{55}^{\circ }+3a+{115}^{\circ }-2a={180}^{\circ }$

$⟹{170}^{\circ }+a={180}^{\circ }$

$⟹a={180}^{\circ }-{170}^{\circ }$

$⟹a={10}^{\circ }$