Two adjacent angles, ∠1

Question

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=__°

Answer 1

To solve for the measures of angles ∠1 and ∠2, we start by setting up an equation based on the information given.

We know:

• \( m\angle 1 = 2x \)
• \( m\angle 2 = 2x + 7 \)
• The sum of these two adjacent angles is 135°.

We can set up the equation: \[ m\angle 1 + m\angle 2 = 135° \] Substituting the expressions for \( m\angle 1 \) and \( m\angle 2 \) into the equation: \[ 2x + (2x + 7) = 135 \]

Now, simplify and solve for \( x \): \[ 2x + 2x + 7 = 135 \] \[ 4x + 7 = 135 \] Subtract 7 from both sides: \[ 4x = 128 \] Divide by 4: \[ x = 32 \]

Now we can find the measures of the angles:

1. For \( m\angle 1 \): \[ m\angle 1 = 2x = 2(32) = 64° \]

2. For \( m\angle 2 \): \[ m\angle 2 = 2x + 7 = 2(32) + 7 = 64 + 7 = 71° \]

Thus, the measures of the two angles are:

• \( m\angle 1 = 64° \)
• \( m\angle 2 = 71° \)

Final answer: m∠1 = 64°, m∠2 = 71°