Question

Two adjacent angles form a resulting angle with measure  160° . m∠1=3x° and m∠2=(2x+10)° . Solve for x . What are the two unknown angles’ measurements?(1 point)
m∠1= ___°, m∠2=____ 

Answer 1

To find the value of \( x \) and the measures of the two angles, we start with the information given in the problem.

The two angles are:
- \( m∠1 = 3x° \)
- \( m∠2 = (2x + 10)° \)

According to the problem, these two angles are adjacent and form a resulting angle of \( 160° \). Therefore, we can set up the equation:

\[
m∠1 + m∠2 = 160°
\]

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

\[
3x + (2x + 10) = 160
\]

Now, simplify this equation:

\[
3x + 2x + 10 = 160
\]
\[
5x + 10 = 160
\]

Next, isolate \( x \) by first subtracting \( 10 \) from both sides:

\[
5x = 160 - 10
\]
\[
5x = 150
\]

Now, divide by \( 5 \):

\[
x = \frac{150}{5}
\]
\[
x = 30
\]

Now that we have \( x = 30 \), we can find the measures of the angles:

For \( m∠1 \):

\[
m∠1 = 3x = 3(30) = 90°
\]

For \( m∠2 \):

\[
m∠2 = 2x + 10 = 2(30) + 10 = 60 + 10 = 70°
\]

Now we confirm if the sum is \( 160° \):

\[
m∠1 + m∠2 = 90° + 70° = 160°
\]

This verification is correct. Thus, the measures of the angles are:

- \( m∠1 = 90° \)
- \( m∠2 = 70° \)

So the final answer is:
- \( m∠1 = 90° \)
- \( m∠2 = 70° \)