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24. ABCDE and PQRST are regular pentagons.

P
E
O
B
Diagram NOT
accurately drawn
R
S
D
C с
SR is parallel to DC
AP = BQ=CR=DS = ET
Work out the size of angle SRC.
You must show all your working.

24. ABCDE and PQRST are regular pentagons. P E O B Diagram NOT accurately drawn R-example-1

1 Answer

3 votes

Answer:

126°

Explanation:

In quadrilateral DSRC, SR || DC (given)

AP = BQ = CR = DS = ET (given)


\therefore CR bisects
\angle DCB


\therefore m\angle DCR=(108\degree)/(2)

(
108\degree is the measure of an angle of pentagon)


\therefore m\angle DCR=54\degree


\because m\angle DCR + m\angle SRC=180\degree

(Measure of interior angles on the same side of transversal)


\therefore 54\degree + m\angle SRC=180\degree


\therefore m\angle SRC=180\degree- 54\degree


\therefore m\angle SRC=126\degree

User Marc Johnston
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