Question

24. ABCDE and PQRST are regular pentagons.
Р
E
-B
T
Diagram NOT
accurately drawn
R
S
D
C
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

The construction of segments AP, BQ, CR, DS, and ET forms five

congruent isosceles trapezoids.

• ∠SRC is 126°

Reasons:

The interior angle of a regular pentagon = 108°

Therefore;

∠SRQ = 108° definition of a regular polygon

Trapezoid SRDC is an isosceles trapezoid by definition of isosceles

trapezoid.

∠DSR ≅ ∠SRC upper base angles of an isosceles trapezoid are congruent.

Trapezoid SRDC is similar to trapezoid QBCR by equal ratio of

corresponding sides,

∠SRC ≅ ∠QRC by CPCFC and substitution property

∠SRC = ∠QRC

∠SRQ + ∠SRC + ∠QRC = 360° sum of angles at a point

108° + ∠SRC + ∠SRC = 360° by substitution property

∠SRC + ∠SRC = 360° - 108°

∠SRC = (360° - 108°) ÷ 2 = 126°

• ∠SRC = 126°

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