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

Question

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

25°
25 degrees

70°
70 degrees

110°
110 degrees

180°

Answer 1

Since the angles are supplementary, their measures add up to \(180^\circ\). Thus, we can set up the following equation:

\[ m∠QRS + m∠SRT = 180° \]

Substituting the given measures:

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

Combining like terms, we get:

\[ 2x + 40 = 180 \]

Next, subtract \(40\) from both sides:

\[ 2x = 180 - 40 \]

\[ 2x = 140 \]

Now, divide by \(2\):

\[ x = 70 \]

Now we can substitute \(x\) back into the expression for \(m∠QRS\):

\[ m∠QRS = x + 40 = 70 + 40 = 110° \]

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