Question

Howdy!

I am here with a handful of geometry questions today. Please answer the question based off the image(s) below.

If you are not sure of the answer please leave a comment, DO NOT ANSWER THE QUESTION UNLESS YOU KNOW THE ANSWER. Please don't take me points! Thanks for understanding.

Anyways, please show all of your work and explain your thinking! This one is not easy! Make sure to answer all 4. There do not upload in order so be specific which answer goes to witch picture! Be sure to answer both steps! Thanks!

Answer 1

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°