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=___ °

1 answer

To find the measures of the angles \( m\angle 1 \) and \( m\angle 2 \), we start with the information given:

  1. The sum of the two adjacent angles is \( 135^\circ \).
  2. The measures of the angles are represented as:
    • \( m\angle 1 = (2x)^\circ \)
    • \( m\angle 2 = (2x + 7)^\circ \)

We can set up the equation:

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

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

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

Now, simplify the left side:

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

This simplifies to:

\[ 4x + 7 = 135 \]

Next, we isolate \( 4x \) by subtracting \( 7 \) from both sides:

\[ 4x = 135 - 7 \]

\[ 4x = 128 \]

Now, divide by \( 4 \):

\[ x = \frac{128}{4} = 32 \]

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

  1. For \( m\angle 1 \):

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

  1. For \( m\angle 2 \):

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

Thus, the measures of the angles are:

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

So the final answer is:

\( m\angle 1 = 64^\circ, \quad m\angle 2 = 71^\circ \)