Solve Equations with Adjacent Angles Practice

Question

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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=

°

Answer 1

Given the adjacent angles \( m∠1 \) and \( m∠2 \) such that their sum is \( 160^\circ \):

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

The equation representing the sum of the angles is:

\[ m∠1 + m∠2 = 160^\circ \]

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

\[ 3x + (2x + 10) = 160 \]

Now, combine like terms:

\[ 3x + 2x + 10 = 160 \]

\[ 5x + 10 = 160 \]

Next, subtract 10 from both sides:

\[ 5x = 150 \]

Now, divide both sides by 5:

\[ x = 30 \]

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

1. \( m∠1 \): \[ m∠1 = 3x = 3(30) = 90^\circ \]

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

Thus, the measurements are:

• \( m∠1 = 90^\circ \)
• \( m∠2 = 70^\circ \)