Question

Two adjacent angles,  ∠1  and  ∠2 , form a resulting angle with measure  135° . If  m∠1=(2x)° and m∠2=(2x+7)° , what are the two unknown angle measures?(1 point)
m∠1= °, m∠2=

Answer 1

To find the measures of angles ∠1 and ∠2, we begin by understanding that their measures are given as follows:

- \( m∠1 = 2x \)
- \( m∠2 = 2x + 7 \)

According to the problem, the sum of these two angles is equal to 135°:

\[
m∠1 + m∠2 = 135°
\]

Substituting the expressions for each angle, we have:

\[
2x + (2x + 7) = 135°
\]

Combining like terms:

\[
4x + 7 = 135°
\]

Next, we isolate the term containing \(x\) by subtracting 7 from both sides:

\[
4x = 135° - 7
\]

\[
4x = 128°
\]

Now, we can solve for \(x\) by dividing both sides by 4:

\[
x = \frac{128°}{4}
\]

\[
x = 32°
\]

Now we can find the measures of angles ∠1 and ∠2.

Substituting \(x\) back into the expressions for the angles:

\[
m∠1 = 2x = 2(32°) = 64°
\]

\[
m∠2 = 2x + 7 = 2(32°) + 7 = 64° + 7° = 71°
\]

Thus, the measures of the two angles are:

\[
m∠1 = 64° \quad \text{and} \quad m∠2 = 71°
\]