Question

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=

°
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:
- \( m∠1 = 90° \)
- \( m∠2 = 70° \)