Question

Two angles are supplementary. They have the following measures: m∠QRS=(x+16)° and m∠SRT=(3x)° . What is the measure of ∠SRT ?(1 point) m∠SRT= ° Remaining Attempts : 3

Answer 1

Two angles are supplementary if their measures add up to \(180^\circ\).

We have:
\[
m∠QRS = (x + 16)^\circ
\]
\[
m∠SRT = (3x)^\circ
\]

Since the angles are supplementary, we can set up the equation:
\[
m∠QRS + m∠SRT = 180^\circ
\]

Substituting the expressions for the angles:
\[
(x + 16) + (3x) = 180
\]

Combining like terms:
\[
4x + 16 = 180
\]

Now, subtract 16 from both sides:
\[
4x = 164
\]

Next, divide by 4:
\[
x = 41
\]

Now that we have the value of \(x\), we can find \(m∠SRT\):
\[
m∠SRT = 3x = 3(41) = 123^\circ
\]

Thus, the measure of \(∠SRT\) is:
\[
\boxed{123}
\]