Question

If m/4=112° and m/7=135°, then find the measures for each of the remaining numbered angles. Justify your answers with definitions and/or theorems.

Answer 1

The measure of the angles are;

m<1 = 68 degrees

m<2 = 112 degrees

m<3 = 45 degrees

m<5 = 68 degrees

m<6 = 45 degrees

To determine the measure of the unknown angles, we need to know the following;

• Complementary angles sum up to 90 degrees
• Supplementary angles sum up to 180 degrees
• Angles on a straight line is equal to 180 degrees
• Alternating angles are equal

Then, we have that;

m<4 + m< 5 = 180

112 + m<5 = 180

m<5 = 68 degrees = m<1

m<2 = 112 degrees

m<7 + m<6 = 180

m<6 = 180 - 135

m<6 = 45 degrees