Question

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.

Answer 1

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`