Question

Two adjacent angles, <1 and <2, form a resulting angle with measure 135. If m<1 = ( 2x ) and m<2 = ( 2x + 7 ) , wut r da two unknown angle measures?

m<1 = ___, m<2 = ___

Answer 1

To determine the measures of the two angles, we first set up an equation based on the information given. We know that:

- \( m\angle 1 = 2x \)
- \( m\angle 2 = 2x + 7 \)

Since angles \( \angle 1 \) and \( \angle 2 \) are adjacent and together form a resulting angle of 135 degrees, we can write the equation:

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

Substituting the expressions for \( m\angle 1 \) and \( m\angle 2 \) into this equation:

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

Now, simplifying the equation:

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

\[
4x + 7 = 135
\]

Next, we subtract 7 from both sides:

\[
4x = 128
\]

Now, divide by 4:

\[
x = 32
\]

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

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

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

Thus, the unknown angle measures are:

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

Final answers:
- \( m\angle 1 = 64 \)
- \( m\angle 2 = 71 \)