In the figure below, AB is a diameter of circle P.
What is the arc measure of ACD in degrees?
(7x+1)
(9x - 7)

317

Step-by-step explanation: By that reasoning, the arc measure of minor arc

AD

⌢

A, D, start superscript, \frown, end superscript is the acute measure of

∠

A

P

D

∠APDangle, A, P, D. We need to find the measure of major arc

ACD

⌢

A, C, D, start superscript, \frown, end superscript.

From the diagram, we see that

∠

A

P

D

∠APDangle, A, P, D,

∠

D

P

C

∠DPCangle, D, P, C and

∠

C

P

B

∠CPBangle, C, P, B are supplementary. The measures of supplementary angles add up to

18

0

∘

180

∘

180, degrees. Thus:

m

∠

A

P

D

+

m

∠

D

P

C

+

m

∠

C

P

D

=

180

(

7

x

+

1

)

+

90

+

(

9

x

−

7

)

=

180

Substitute.

16

x

+

84

=

180

Collect like terms.

16

x

=

96

Subtract

84.

x

=

6

Divide by

16.

m∠APD+m∠DPC+m∠CPD

(7x+1)+90+(9x−7)

16x+84

16x

x

=180

=180

=180

=96

=6

Substitute.

Collect like terms.

Subtract 84.

Divide by 16.

We can use the value of

x

xx to evaluate the measure of

∠

A

P

D

∠APDangle, A, P, D. Let's substitute in our value for

x

xx.

m

∠

A

P

D

=

(

7

x

+

1

)

∘

=

(

7

(

6

)

+

1

)

∘

=

4

3

∘

m∠APD

=(7x+1)

∘

=(7(6)+

43

Step-by-step explanation:

take (7x + 1) + 90 (the square) + (9x - 7) = 180

what