Question

find the value in the figure​

Answer 1

Answer:

330 degerr

Step-by-step explanation:

a+80=180

a=100........

c+90=180

c=90.........

b+150=180

b=30........

d+ 70=180

d=110.....................................

add a,b,c,d

100+110+90+30=330

hence proved

Answer 2

Given:

➝ ∠EDC = 70°

➝ ∠DCB = 90°

➝ ∠CBA = 150°

➝ ∠BAE = 80°

Concepts we'll be using to solve the question:

➝ Linear Pair.

➝ Angle Sum Property of a quadrilateral.

Solution:

On line AE:

➝ ∠a + ∠BAE = 180° (Linear Pair)

➝ ∠a + 80° = 180°

➝ ∠a = 180° - 80°

➝ ∠a = 100°

On line AB:

➝ ∠b + ∠ABC = 180° (Linear Pair)

➝ ∠b + 150° = 180°

➝ ∠b = 180° - 150°

➝ ∠b = 30°

On line BC:

➝ ∠c + ∠DCB = 180° (Linear Pair)

➝ ∠c + 90° = 180°

➝ ∠c = 180° - 90°

➝ ∠c = 90°

On line DC:

➝ ∠d + ∠EDC = 180° (Linear Pair)

➝ ∠d + 70° = 180°

➝ ∠d = 180° - 70°

➝ ∠d = 110°

In polygon ABCDE,

➝ ∠A + ∠B + ∠C + ∠D + ∠E = 540° (ASP of a Pentagon)

➝ 80° + 150° + 90° + 70° + ∠E = 540°

➝ 390° + ∠E = 540°

➝ ∠E = 540° - 390°

➝ ∠E = 150°

On line AE:

➝ ∠e + ∠AED = 180° (Linear Pair)

➝ ∠e + 150° = 180°

➝ ∠e = 180° - 150°

➝ ∠e = 30°

Now, we have to find ∠a + ∠b + ∠c + ∠d + ∠e.

➝ ∠a + ∠b + ∠c + ∠d + ∠e

➝ 100° + 30° + 90° + 110° + 30°

➝ 360°

∴ ∠a + ∠b + ∠c + ∠d + ∠e = 360°