Question

Triangle ABC is formed by two parallel lines and two other intersecting lines.

Find the measure of each angle A, B, and C of the triangle.

STEP ONE: Use what you know about vertical angles to find angle C

C =
HINT: angle C is vertical to an angle of 47 degrees.

STEP TWO: Use what you now about linear angles to find angle B.

B =
HINT: 61 + 47 plus angle B must equal 180 degrees

STEP THREE: Now that you know angles B and C, use what you know about missing angles in triangles to find angle A.

A =
HINT: angle A + angle B + angle C = 180 degrees

Answer 1

Step 1: Find angle C

Vertical angles are congruent. Angle C and the lower right angle measuring 47 degrees are vertical angles. Therefore angle C = 47 degrees.

Step 2: Find angle B

Angle B, the upper right 47 degree angle, and 61 degree angle all form a straight line. A straight line is 180 degrees.

B + 47 + 61 = 180

B + 108 = 180

B = 72 degrees

Step 3: Find angle A

The sum of the interior angles of a triangle is 180 degrees. The sum of angles a, b, and c will be 180 degrees.

A + B + C = 180

A + 72 + 47 = 180

A + 119 = 180

A = 61 degrees

Answers:

A = 61 degrees

B = 72 degrees

C = 47 degrees

Hope this helps!