Question

12 a. give an appropriate name describing the relationship between \\( \angle 6 \\) and \\( \angle 7 \\).

o corresponding angles; congruent
o vertical angles; congruent
same - side exterior angles; supplementary
same - side interior angles; supplementary
12c. record the measure of all the angles in the diagram. given that \\( m \angle 6 = 95 ^ { \circ } \\).
\\( \angle 1, \angle 3, \angle 6 \\), and \\( \angle 8 \\) are \\( \square \\) degrees.
\\( \angle 2, \angle 4, \angle 5 \\), and \\( \angle 7 \\) are \\( \square \\) degrees.

Explanation:

Step1: Determine the relationship between ∠6 and ∠7

Same - side interior angles are two angles that are on the same side of the transversal and between the two parallel lines. ∠6 and ∠7 are on the same side of the transversal and between the two parallel lines, and they are supplementary (their sum is \(180^{\circ}\)).

Step2: Calculate the measure of angles

Given \(m\angle6 = 95^{\circ}\)

• For \(∠1,∠3,∠6,∠8\):

\(∠1\) and \(∠3\) are vertical angles with \(∠6\) and \(∠8\) respectively. Vertical angles are congruent. So \(m\angle1=m\angle3 = m\angle6=m\angle8=95^{\circ}\)

• For \(∠2,∠4,∠5,∠7\):

Since \(∠6\) and \(∠7\) are supplementary (\(∠6 + ∠7=180^{\circ}\)), then \(m\angle7=180 - 95=85^{\circ}\). \(∠2\) and \(∠4\) are vertical angles with \(∠5\) and \(∠7\) respectively. Vertical angles are congruent. So \(m\angle2=m\angle4=m\angle5=m\angle7 = 85^{\circ}\)

Answer:

12a. same - side interior angles; supplementary
12c. \(95\), \(85\)