MAT1793-ABED_1: Combining Properties

Constructing Knowledge

You can use a combination of transversal properties to calculate unknown angle measures when multiple transversals are crossing parallel lines. In order to calculate unknown angle measures, it is helpful to remember additional properties involved with lines and angles.

One of the most common, and very important, is the interior angles of a triangle add up to 180°.

EXAMPLE

Determine the measure of angles A, B, and C in the diagram. Provide an explanation of how the angle measure is determined using appropriate terminology and properties.

Solution

Angle	diagram	Transversal rules used	Angle
B		Angle B corresponds to the 60° that is given in the original diagram.	∠B is 60°.
C		The angle adjacent to the 135° in the original diagram is supplementary with 135°. Therefore, its measure is 45°, as indicated. This 45° angle corresponds to angle C.	∠C is 45°.
A		Once angles B and C are known, the angle at the top of the triangle can be determined to be 75° because the sum of the interior angles of a triangle add to 180°. The vertically opposite angle to the 75°angle is angle A.	∠A is 75°.