Question

ABCDE is a regular Pentagon and Bp and DQ are the angle bisectors of b and d respectively find angle PRD​

Answer 1

Current Question.

ABCDE is a regular Pentagon and Angle BP and Angle DQ are the angle bisectors Angle B and Angle D respectively find angle PRD

SOLUTION

Measure of an interior angle of a regular polygon

$\rm : \to \: \frac{(n - 2) \times 180 \degree}{n}$

Measure of one interior angle of a regular pentagon

$\rm : \to\frac{(5 - 2) \times 180 \degree}{5} = 3 \times 36 \degree \: = 108 \degree$

Thus, in quadrilateral BCDP, Angle BPD

= 360° - (Angle PBC + Angle BCD + Angle CDP)

= 360° - (54°+108°+108°)

(°•° Angle PBC = AngleCDP / 2 108°/2 = 54°)

= 360° - 270°

= 90°

In ∆ PRD , Angle PRD = 180°-(Angle RDP+ Angle DPR)

= 180° - ( Angle RDP+ Angle BPD)

(°•° Angle DPR = Angle BPD)

= 180° - (54° + 90°)

(°•° Angle RDP = 108°/2 = 54°)

= 180° - 144°

= 36°