Two angles are supplementary and have measures m∠QRS=(x+40)°

Question

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

Answer 1

Two angles are supplementary if the sum of their measures is 180 degrees. Given:

\[ m∠QRS = (x + 40)° \] \[ m∠SRT = x° \]

We can set up the equation:

\[ m∠QRS + m∠SRT = 180° \]

Substituting the expressions for the angles:

\[ (x + 40) + x = 180 \]

Combine like terms:

\[ 2x + 40 = 180 \]

Now, subtract 40 from both sides:

\[ 2x = 180 - 40 \] \[ 2x = 140 \]

Divide both sides by 2:

\[ x = 70 \]

Now that we have the value of \(x\), we can find the measure of \(m∠QRS\):

\[ m∠QRS = x + 40 = 70 + 40 = 110° \]

Therefore, the measure of \(∠QRS\) is \( \boxed{110} \) degrees.