Question

CR and DS are perpendiculars dropped from AB to PQ , and AB is perpendicular to CR and DS . If CR = DS, which statement must be true?

A.) m∠RCD = m∠SDB ÷ 2

B.) m∠RCD = m∠ACD

C.) m∠RCD = m∠ACD ÷ 2

D.) m∠RCD = m∠ACD ÷ 3

E.) m∠RCD = m∠ACD × 2

Answer 1

The answer is C.) m∠RCD = m∠ACD ÷ 2

RCD = ACD divided by two.

RCD = 90 degrees.

ACD÷2 = 180÷2 = 90 degrees.

So, your answer is C.

Hope this helped. Have a great day!

Answer 2

Optin C. m∠RCD = m∠ACD ÷ 2

Explanation:

CR and DS are the perpendiculars dropped from Ab and PQ.

CR = DS is given in the question.

we have to tell the true statement given in the options.

Since sum of all angles at a given point on a straight line is 180°

m∠ACD = m∠ACR + m∠RCD = 180°

it is given that m∠ACR = m∠RCD (CR is perpendicular to AB and PQ both)

Therefore m∠ACD = 2× m∠RCD

⇒ m∠RCD = m∠ACD ÷ 2

Therefore Option C). is the answer.