In the figure below, \overline{AD} AD start overline, A, D, end overline and \overline{BE} BE start overline, B, E, end overline
are diameters of circle PPP. What is the arc measure of \stackrel{\LARGE{\frown}}{CD} CD ⌢ C, D, start superscript, \frown, end superscript in degrees? ^\circ ∘ degrees
2 answers:
Answer:
<u>The measure of the arc CD = 64°</u>
Step-by-step explanation:
The rest of the question is the attached figure.
It is required to find the measure of the arc CD in degrees.
as shown at the graph
BE and AD are are diameters of circle P
And ∠APE is a right angle ⇒ ∠APE = 90°
∠APE and ∠BPE are supplementary angles
So, ∠APE + ∠BPE = 180°
∠BPE + 90 = 180°
∴ ∠BPE = 180 -90 = 90° ⇒(1)
But it is given: ∠BPE = (33k-9)° ⇒(2)
From (1) and (2)
∴ 33k - 9 = 90
∴ 33k = 90 + 9 = 99
∴ k = 99/33 = 3
The measure of the arc CD = ∠CPD = 20k + 4
By substitution with k
<u>∴ The measure of the arc CD = 20*3 + 4 = 60 + 4 = 64°</u>
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