Question

solve.
use the diagram shown to solve problems 3–5.
3 in the diagram, lines ( a ) and ( b ) are parallel, with ( mangle 3 = 65^circ ) and ( mangle 11 = 100^circ ). find the measures of ( angle 2 ), ( angle 5 ), and ( angle 13 ). tell which angle relationships you used to help you find each measure.
( mangle 2 ):
( mangle 5 ):
( mangle 13 ):

Explanation:

For \( m\angle 2 \):

Step 1: Identify angle relationship

\(\angle 2\) and \(\angle 3\) are supplementary (linear pair), so \(m\angle 2 + m\angle 3 = 180^\circ\).

Step 2: Substitute \(m\angle 3 = 65^\circ\)

\(m\angle 2 + 65^\circ = 180^\circ\)

Step 3: Solve for \(m\angle 2\)

\(m\angle 2 = 180^\circ - 65^\circ = 115^\circ\)

For \( m\angle 5 \):

Step 1: Identify angle relationship

\(\angle 3\) and \(\angle 5\) are alternate interior angles (since \(a\parallel b\) and \(d\) is transversal), so \(m\angle 5 = m\angle 3\).

Step 2: Substitute \(m\angle 3 = 65^\circ\)

\(m\angle 5 = 65^\circ\)

For \( m\angle 13 \):

Step 1: Identify angle relationship

\(\angle 11\) and \(\angle 13\) are corresponding angles (since \(a\parallel b\) and \(c\) is transversal), so \(m\angle 13 = m\angle 11\).

Step 2: Substitute \(m\angle 11 = 100^\circ\)

\(m\angle 13 = 100^\circ\)

Answer:

s:

• \(m\angle 2 = \boldsymbol{115^\circ}\) (supplementary angles)
• \(m\angle 5 = \boldsymbol{65^\circ}\) (alternate interior angles)
• \(m\angle 13 = \boldsymbol{100^\circ}\) (corresponding angles)