Question

Angles U and V are supplementary angles. The ratio of their measures is 7:13 Find the measure of each angle

Answer 1

If
`u` and
`v` are supplementary angles, then


`u+v=180^(\circ)~~~~~\mathbf{(i)}`


The ratio of
`u` and
`v` is
`(7)/(13):`


`(u)/(v)=(7)/(13)\\\\\\ u=(7v)/(13)~~~~\mathbf{(ii)}`


Substitute
`\mathbf{(ii)}` into
`\mathbf{(i)}:`


`(7v)/(13)+v=180^(\circ)\\\\\\ \left((7)/(13)+1 \right )\cdot v=180^(\circ)\\\\\\ \left((7)/(13)+(13)/(13) \right )\cdot v=180^(\circ)\\\\\\ (20)/(13)\cdot v=180^(\circ)\\\\\\ v=180^(\circ)\cdot (13)/(20)\\\\\\ \boxed{\begin{array}{c} v=117^(\circ) \end{array}}`


From
`\mathbf{(i)},` we find the measure of
`u:`


`u=180^(\circ)-v\\\\ u=180^(\circ)-117^(\circ)\\\\ \boxed{\begin{array}{c} u=63^(\circ) \end{array}}`