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

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

70°
70 degrees

25°
25 degrees

110°
110 degrees

180°

1 answer

If two angles are supplementary, their measures add up to 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:

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

Now, divide by 2:

\[ x = 70 \]

Now we can find the measure of \( m∠QRS \):

\[ m∠QRS = x + 40 = 70 + 40 = 110° \]

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