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

Optin C. m∠RCD = m∠ACD ÷ 2

Step-by-step 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.

(2/5)(x-1)<(3/5)(x+1)  perform indicated multiplications

(2x-2)/5<(3x+3)/5  multiply both sides by 5

2x-2<3x+3  add 2 to both sides

2x<3x+5  subtract 3x from both sides

-x<5  divide both sides by -1  (remember to reverse direction of inequality sign when multiplying/dividing by a negative value)

x>-5