Question

please answer fast please step by step​

Answer 1

Answer:

∠a = 90°

∠b = 75°

Step-by-step explanation:

∠a is the exterior angle of ∆QXY so sum of ∠QXY and ∠QYX will be the sum of ∠a. It is a universal truth (Theorem) for any triangle.

so

∠QXY + ∠QYX = ∠a

=> 55°+35° = ∠a

=> ∠a = 90°

∠a = ∠XQZ

Now Sum of all angles of ∆XYZ = 180°

so

∠XQZ + ∠QZX + ∠QXZ = 180°

=> ∠a + 40° + ∠QXZ = 180°

=> 90°+40° + ∠QXZ = 180°

=> 130° + ∠QXZ = 180°

=> ∠QXZ = 180°-130° = 50°

Now line PXY contains angles ∠PXZ, ∠QXZ, ∠QXY.

here ∠PXZ = ∠b, ∠QXZ = 50°, ∠QXY = 55°

A straight line = 180°

so

∠PXZ + ∠QXZ + ∠QXY = 180°

=> ∠b + 50°+55° = 180°

=> ∠b + 105° = 180°

=> ∠b = 180°-105°

=> ∠b = 75°

Hence ∠a = 90° and ∠b = 75°.

hope it helps.

Answer 2

Answer:

In triangle XYQ

a° = 55° + 35° (Exterior Angle Property of a triangle)

a° = 90°

In triangle XQZ

a° + 40° + angle QXZ = 180° (Angle Sum Property of a triangle)

=> 90° + 40° + QXZ = 180°

=> QXZ = 50°

PXY is a straight line

b° + 50° + 55° = 180° (Angles on a straight line at a point)

=> b° = 75°

Hence, a = 90°, b = 75°