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miv72 [106K]
3 years ago
5

In the adjoining figure, GP bisects angle BGH and HP bisects angle GHD. calculate the size of angle a.​

Mathematics
1 answer:
Volgvan3 years ago
6 0

Answer:

90°

Step-by-step explanation:

AB and  CD are parallel lines and EF is reversal

Therefore angles BGH and DHG are consecutive interior angles

<u>As we know the sum of consecutive interior angles equals to 180°:</u>

  • ∠BGH + ∠DHG = 180°

<u>Line GP bisects angle BGH , therefore</u>

  • m∠PGH = 1/2*m∠BGH

<u>Line HP bisects angle GHD, therefore</u>

  • m∠PHG = 1/2*m∠GHD

<u>Sum of two angles of triangle GHP:</u>

  • m∠PGH + m∠GHD = 1/2(∠BGH + ∠DHG) = 1/2*180° = 90°

<u>Therefore the missing angle a is:</u>

  • ∠a = 180° - (m∠PGH + m∠GHD) = 180° - 90° = 90°
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