Two adjacent angles form a resulting angle with measure 160°

Question

. m∠1=3x°
and m∠2=(2x+10)°
. Solve for x
. What are the two unknown angles’ measurements?(1 point)
m∠1=

°
, m∠2=

°
Remaining Attempts : 3

Answer 1

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

1. The sum of the two angles is 160°: \[ m∠1 + m∠2 = 160° \]

2. The measures of the angles are defined as:

   • \( m∠1 = 3x \)
   • \( m∠2 = 2x + 10 \)

Now, we substitute these expressions into the equation from step 1: \[ 3x + (2x + 10) = 160 \]

Simplifying this, we combine like terms: \[ 3x + 2x + 10 = 160 \] \[ 5x + 10 = 160 \]

Next, we isolate \( x \) by subtracting 10 from both sides: \[ 5x = 160 - 10 \] \[ 5x = 150 \]

Now, divide both sides by 5: \[ x = \frac{150}{5} = 30 \]

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

1. Calculate \( m∠1 \): \[ m∠1 = 3x = 3(30) = 90° \]

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

Thus, the two unknown angles are:

• \( m∠1 = 90° \)
• \( m∠2 = 70° \)

To summarize:

• \( m∠1 = 90° \)
• \( m∠2 = 70° \)