Question

Two adjacent angles from resulting angle with measures 160. m <1 = 3x and m <2 = ( 2x + 10 ). Solve for x What are the two unknown angles' measurements?


m<1 = _, m <2 = _

Answer 1

To find the value of \( x \) and the measures of the two angles, we start with the given equations for the angles:

- \( m \angle 1 = 3x \)
- \( m \angle 2 = 2x + 10 \)

We know that the sum of the measures of the two angles is 160 degrees, so we can set up the equation:

\[
m \angle 1 + m \angle 2 = 160
\]

Substituting the expressions for the angles into the equation gives us:

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

Now, combine like terms:

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

Next, subtract 10 from both sides:

\[
5x = 150
\]

Now, divide by 5:

\[
x = 30
\]

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

For \( m \angle 1 \):

\[
m \angle 1 = 3x = 3(30) = 90
\]

For \( m \angle 2 \):

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

Thus, the measures of the two angles are:

\[
m \angle 1 = 90^\circ, \quad m \angle 2 = 70^\circ
\]

Final answer:
- \( m \angle 1 = 90^\circ \)
- \( m \angle 2 = 70^\circ \)