Question

relating angles of a straight line to angles in a triangle
examine the diagram.
find the interior angles of the triangle.
which kind of angle pair is ∠a and the angle marked 70°?
what is the measurement of each angle?
m∠a =
m∠b =
m∠c = 10, 30, 70, 80

Explanation:

Step1: Identify Angle Pair Type

∠A and the 70° angle are alternate interior angles (since lines are parallel, cut by transversal AB), so they are equal. So the angle pair is alternate interior angles.

Step2: Find m∠B

Angles on a straight line sum to 180°. So \( m\angle B = 180^\circ - 70^\circ - 30^\circ = 80^\circ \).

Step3: Find m∠A

From alternate interior angles, \( m\angle A = 70^\circ \).

Step4: Find m∠C

Triangle angle sum is 180°. So \( m\angle C = 180^\circ - m\angle A - m\angle B = 180^\circ - 70^\circ - 80^\circ = 30^\circ \).

Answer:

Angle pair: Alternate Interior Angles
\( m\angle A = 70^\circ \)
\( m\angle B = 80^\circ \)
\( m\angle C = 30^\circ \)