Question

The measure of two supplematry angles

Answer 1

Given that angles S and T are supplementary, then:

m∠S + m∠T = 180°

Given that angles S and T are in the ratio 7:3, then:

`(m\angle S)/(m\angle T)=(7)/(3)`

Isolating m∠T from the first equation:

m∠T = 180° - m∠S

Substituting this into the second equation, and solving for m∠S:

`\begin{gathered} (m\angle S)/(180-m\angle S)=(7)/(3) \\ m\angle S\cdot3=7\cdot(180-m\angle S) \\ 3m\angle S=7\cdot180-7m\angle S \\ 3m\angle S+7m\angle S=1260 \\ 10m\angle S=1260 \\ m\angle S=(1260)/(10) \\ m\angle S=126\text{ \degree} \end{gathered}`