Two angles are supplementary. They have the following measures: m∠QRS=(x+16)°

Question

and m∠SRT=(3x)°
. What is the measure of ∠SRT
?(1 point)
m∠SRT=

°

Answer 1

Two angles are supplementary if their sum equals \(180^\circ\). Given the measures of the angles:

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

We can set up the equation for their sum:

\[ (x + 16) + (3x) = 180 \]

Combining like terms gives:

\[ 4x + 16 = 180 \]

Next, we will isolate \(x\) by subtracting 16 from both sides:

\[ 4x = 180 - 16 \] \[ 4x = 164 \]

Now, divide by 4:

\[ x = \frac{164}{4} = 41 \]

Now that we have \(x\), we can find the measure of angle \(SRT\):

\[ m∠SRT = 3x = 3(41) = 123 \]

Thus, the measure of \(∠SRT\) is:

\[ \boxed{123^\circ} \]