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=

1 answer

To solve for \( x \), we know that the sum of the two adjacent angles equals the resulting angle of 160°:

\[ m∠1 + m∠2 = 160° \]

Given: \[ m∠1 = 3x° \quad \text{and} \quad m∠2 = (2x + 10)° \]

We can substitute these expressions into the equation:

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

Now, combine like terms:

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

\[ 5x + 10 = 160 \]

Next, subtract 10 from both sides:

\[ 5x = 150 \]

Now, divide by 5:

\[ x = 30 \]

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

\[ m∠1 = 3x = 3(30) = 90° \]

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

Thus, the measurements of the two angles are:

\[ m∠1 = 90° \quad \text{and} \quad m∠2 = 70° \]

To summarize:

  • \( m∠1 = 90° \)
  • \( m∠2 = 70° \)