We know that Sum of Angles in a Triangle = 180
⇒ Angle(4) + Angle(5) + Angle(7) = 180
⇒ 52 + 44 + Angle(7) = 180
⇒ 96 + Angle(7) = 180
⇒ Angle(7) = 180 - 96 = 84
We know that Vertically Opposite Angles are Equal
Angle(7) and Angle(10) are Equal
⇒ Angle(10) = 84
Also, Angle(8) and Angle(9) are Equal
Let us take Angle(8) = Angle(9) = P
As Angle(8) - Angle(9) - Angle(7) - Angle(10) form a Complete Angle, their Sum should be Equal to 360.
⇒ Angle(8) + Angle(9) + Angle(7) + Angle(10) = 360
⇒ P + P + 84 + 84 = 360
⇒ 2P + 168 = 360
⇒ 2P = 192
⇒ P = 96
We took Angle(8) = Angle(9) = P
⇒ Angle(8) = Angle(9) = 96