Question

Howdy!

Answer 1

Answer:

A) Central angle has same measure as intercepted arc.

• mCE = mCD + mDE = 20° + 90° = 110°

B) Opposite angles of cyclic quadrilateral are supplementary.

• mRL = 2*m∠PQR - mPL = 2*74° - 72° = 76°
• m∠QPL = (1/2)mQRL = (1/2)(90° + 76°) = 83°
• m∠QRL = 180° - m∠QPL = 180° - 83° = 97°
• mQP = 360° - (90° + 76° + 72°) = 122°

C)

• m∠MLN = m∠MRN as same arc MN is intercepted
• m∠LMN is right angle as opposite side is diameter.
• ∠MNL is complementary with ∠MLN which is same as ∠MRN
• m∠MNL = 90° - 47° = 43°

D) Tangent secant angle is half of the intercepted arc.

It seems wrong. Should be mQP instead of mQR

• mQP = 2*m∠RQP = 2*74° = 148°