Question

IN TRIANGLE XYZ, XY = XZ. A STRAIGHT LINE CUTS XZ AT P, YZ AT Q AND XY PROUCED AT R. IF YQ=YR AND QP=QZ.FIND ANGLES OF THE TRIANGLE XYZ

Answer 1

There is a mistake in the question. Angle YXZ and angle YZX are be found.

The student has mentioned angle YXZ and angle YXZ but it wrong. I have tried my best to solve it.

Solution:-

Sin x = opposite side of x/hypotenuse

⇒ x/2x = 1/2

Sin x = 1/2 = Sin 30°

⇒ x = 30° or ∠ YXZ = 30°

Cos Z = Adjacent side of z/hypotenuse

⇒ x/2x = 1/2 

⇒ Cos Z = 1/2 = Cos 60°

Z = 60° = ∠ YZX = 60°  Answer.