Question

In the diagram below, AC ICB, AB I CD, and mZA = 31°. Find mZB.

С
D
B
You may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.

Answer 1

m∠B = 59°

Explanation:

From ΔADC,

m∠DAC = 31°

By triangle sum theorem,

m∠ADC + m∠DAC + m∠DCA = 180°

90° + 31° + m∠DCA = 180°

m∠DCA = 180° - 121°

= 59°

m∠ACB = m∠ACD + m∠BCD

90° = m∠ACD + 59°

m∠ACD = 90° - 59°

= 31°

In ΔCDB,

m∠CDB + m∠DBC + m∠DCB = 180°

90° + m∠DBC + 31° = 180°

m∠DBC = 180° - 121°

= 59°

Therefore, measure of angle B = 59°.