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

Question

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Answer 1

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

• m∠QRS = (x + 40)°
• m∠SRT = x°

Since the angles are supplementary, we have the equation:

$$m\angle QRS+m\angle SRT=180°$$

Substituting the expressions for the angles:

$$(x+40)+x=180$$

Now, combine like terms:

$$2x+40=180$$

Next, subtract 40 from both sides:

$$2x=140$$

Then, divide by 2:

$$x=70$$

Now that we have the value of $x$, we can find the measure of ∠QRS:

$$m\angle QRS=x+40=70+40=110°$$

Thus, the measure of ∠QRS is $110°$.