Question

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

Answer 1

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

As we know the sum of consecutive interior angles equals to 180°:

• ∠BGH + ∠DHG = 180°

Line GP bisects angle BGH , therefore

• m∠PGH = 1/2*m∠BGH

Line HP bisects angle GHD, therefore

• m∠PHG = 1/2*m∠GHD

Sum of two angles of triangle GHP:

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

Therefore the missing angle a is:

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