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 the angles \( m\angle 1 \) and \( m\angle 2 \), we start with the information given:

1. The sum of the two adjacent angles is \( 135^\circ \).
2. The measures of the angles are represented as:
- \( m\angle 1 = (2x)^\circ \)
- \( m\angle 2 = (2x + 7)^\circ \)

We can set up the equation:

\[
m\angle 1 + m\angle 2 = 135^\circ
\]

Substituting in the expressions for \( m\angle 1 \) and \( m\angle 2 \):

\[
2x + (2x + 7) = 135
\]

Now, simplify the left side:

\[
2x + 2x + 7 = 135
\]

This simplifies to:

\[
4x + 7 = 135
\]

Next, we isolate \( 4x \) by subtracting \( 7 \) from both sides:

\[
4x = 135 - 7
\]

\[
4x = 128
\]

Now, divide by \( 4 \):

\[
x = \frac{128}{4} = 32
\]

Now that we have \( x \), we can find the measures of the angles:

1. For \( m\angle 1 \):

\[
m\angle 1 = 2x = 2(32) = 64^\circ
\]

2. For \( m\angle 2 \):

\[
m\angle 2 = 2x + 7 = 2(32) + 7 = 64 + 7 = 71^\circ
\]

Thus, the measures of the angles are:

\[
m\angle 1 = 64^\circ, \quad m\angle 2 = 71^\circ
\]

So the final answer is:

\( m\angle 1 = 64^\circ, \quad m\angle 2 = 71^\circ \)