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=____ 

1 answer

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:

  • \( m∠1 = 90° \)
  • \( m∠2 = 70° \)