Question

In the figure, find the measures of x and y.​

Answer 1

/B and /D are linear pair angles

/B+/D = 180°

/B + 65° = 180°

/B = 180° -65°

/B = 115° = x

apply angle sum property in /\ ABC

/A+/B+/C= 180°

Y + 115° + 30° = 180°

Y= 180° - 145°

Y= 45°

•°• x = 115°

y = 45°

hope this will help you.

Answer 2

x = 115°

y = 35°

Given

∠ABC : x°

∠BCA : 30°

∠CÀB : y°

∠CBD : 65°

To Find

∠ABC : x°

∠CÀB : y°

Calculation

∠CBD + ∠ABC = 180°

Because, they are Linear Pair . (non common arms are opposite to each other)

So, ∠CBA + ∠ABC = 180°

65° + ∠ABC = 180

∴∠ABC = 180 - 65 = 115°

x° = 115

In ABC, ∠A + ∠B + ∠C = 180°

According to Angle Sum Property of a Triangle sum of all the angles of a Triangle = 180°

So, ∠A + ∠B + ∠C = 180°

∠A + 115 + 30 = 180

∠A + 145 = 180

∴∠A = 180 - 145 = 35°

y° = 35°

Have a good day :)