Question

Bryce drew a rectangle and labeled five of the angles, as shown. He knew these factsabout the angles:• The measurements of angles 1 and 3 are the same.• The measurement of angle 2 equals 110°.• The measurements of angles 3 and 5 are the same.What is the measure of angle 1,3,4, and 5?

Answer 1

As shown in the figure, Angle 1, 2, and 3 combined makes a straight angle and a straight angle measures 180 degrees.

If Angle 2 is equal to 110 degrees, then Angle 1 and Angle 3 combined is 180 - 110 = 70 degrees.

If Angle 1 and 3 have the same measurement, then we can divide 70 degrees by 2 to get the measure of each angle. Therefore, both Angle 1 and 3 measures 35 degrees.

Angle 4 and Angle 5 combined forms a right angle and a right angle measures 90 degrees.

If Angle 3 and Angle 5 measures the same, then Angle 5 is also 35 degrees.

If Angle 5 is 35 degrees, then Angle 4 is 90 - 35 = 55 degrees. Angle 4 measures 55 degrees.