By applying the supplementary angle theorem, the magnitude of angle B (m<B) is equal to 38°.
What is a supplementary angle?
A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees.
Mathematically, a supplementary angle can be calculated by using this formula:
Q + R = 180
Where:
Q and R are measure of the angles subtended.
m<ADC = 180° - 110°
m<ADC = 70°
Substituting the given parameters into the formula, we have;
m<ADC + m<DAC + m<ACB = 180
70 + 46 + m<ACB = 180
116 + m<ACB = 180
m<ACB = 180 - 116
m<ACB = 64°
Now, we can determine the magnitude of angle B (m<B) based on the given diagram:
m<B = 180 - (m<CAB + m<ACB)
m<B = 180 - (78 + 64)
m<B = 180 - 142
m<B = 38°
Read more on supplementary angle here: https://brainly.com/question/11042147
#SPJ1
