Two angles are supplementary and have measures  m∠QRS=(x+40)° and m∠SRT=x° . What is the measure of ∠QRS ?(1 point)

Responses

180°
  180 degrees

25°
  25 degrees

70°
  70 degrees

110

Pls get it right thx

1 answer

To find the measures of the angles, we start with the information that two angles are supplementary. This means that the sum of the two angles is 180 degrees. Given:

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

We can set up the equation:

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

Simplifying this gives:

\[ 2x + 40 = 180 \]

Subtracting 40 from both sides:

\[ 2x = 140 \]

Dividing both sides by 2:

\[ x = 70 \]

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

\[ m∠QRS = x + 40 = 70 + 40 = 110° \]

Therefore, the measure of \( ∠QRS \) is:

\[ \boxed{110°} \]