Question

Where mBD =70° and mCA = 170°

Answer 1

Answer:

m∠BPD = 120

mBC + mAD = 120°

Step-by-step explanation:

according to intersecting chord theorem: The measure of the angle formed by two chords  that intersect inside the circle is $\frac{1}{2}$ the sum of the chords' intercepted arcs.

m∠BPD = $\frac{1}{2}$ (M∠BD + M∠CA)

             = $\frac{1}{2}$  (70 + 170)

             =  $\frac{1}{2}$ (240)

m∠BPD = 120

We know that a circle has a total of 360° around the center of circle. To find the measure of the remaining measure of angle of arcs, subtract them from the whole that is 360°

mBC + mAD = 360 - ( 70 + 170 )

                     = 360 - 240

mBC + mAD = 120°