Question

Find the value of x and y in the following figures

Answer 1

Answer:

1) x = 60° and y = 50°

2) x = 45°  and y = 45°.

Step-by-step explanation:

1) 70° + x = 130° (Exterior angle property)

=> x = 130° - 70° = 60°

Now, 70° + x + y = 180° (Angle sum property)

=> 70° + 60° + y = 180°

=> 130° + y = 180°

=> y = 180° - 130° = 50°

x = 60° and y = 50°

2) In ∆ADC,

∠CAD = 50°

∠CDA = 85°

∠DCA = ?

Sum of all the angle of a triangle = 180°

∠CAD + ∠CDA + ∠DCA = 180°

= 50° + 85° + y = 180°

= 135° + y = 180°

=> y = 180° - 135°

=> y = 45°

Measure of ∠CDB,

∠CDB + ∠CDA = 180°  [linear pair]

= ∠CDB + 85° = 180°

=> ∠CDB = 180°-85°

=> ∠CDB = 95°

Now,  In ∆CDB

∠CDB = 95°

∠CBD = x

∠DCB = 40°

∠CDB + ∠CBD + ∠DCB = 180° [Angle - Sum Property of a triangle]

= 95° + x + 40° = 180°

=> 135° + x = 180°

=> x = 180° - 135°

=> x = 45°

Therefore the value of x and y are:-

x = 45°  and y = 45°.