Question

Where mBD =70° and mCA = 170°

Answer 1

m∠BPD = 120

mBC + mAD = 120°

Explanation:

according to intersecting chord theorem: The measure of the angle formed by two chords that intersect inside the circle is
`(1)/(2)` the sum of the chords' intercepted arcs.

m∠BPD =
`(1)/(2)` (M∠BD + M∠CA)

=
`(1)/(2)` (70 + 170)

=
`(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°