Answer:
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)+
Answer:
43
Step-by-step explanation:
take (7x + 1) + 90 (the square) + (9x - 7) = 180
