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 two adjacent angles \( \angle 1 \) and \( \angle 2 \), we can use the information provided in the problem.

Given:
- \( m\angle 1 = 2x \)
- \( m\angle 2 = 2x + 7 \)
- The angles form a resulting angle of \( 135^\circ \).

Since the angles are adjacent, we can write the equation for their sum:

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

Substituting the expressions for the angles into the equation:

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

Now, simplify and solve for \( x \):

\[
2x + 2x + 7 = 135
\]
\[
4x + 7 = 135
\]
\[
4x = 135 - 7
\]
\[
4x = 128
\]
\[
x = 32
\]

Now we can find the measures of each angle:

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

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

Therefore, the measures of the angles are:
\[
m\angle 1 = 64^\circ \quad \text{and} \quad m\angle 2 = 71^\circ
\]