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:

$\frac{m\angle S}{m\angle T}=\frac{7}{3}$

Isolating m∠T from the first equation:

m∠T = 180° - m∠S

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

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