Find the value of x and y in the following figures

Answers
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°.