Question

can you plss find this angles magnitude ​

Answer 1

a) ∠EDC = 30°

b) ∠ADE = 50°

c) ∠B = 50°

d) ∠AED = 80°

e) ∠ACB = 80°

Step-by-step explanation:

GIVEN

∠A = 50°

∠BDC = 100°

∠BCD = 30°

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TO FIND

a) ∠EDC

b) ∠ADE

c) ∠B

d) ∠AED

e) ∠ACB

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∠B

We know that,

Sum of all interior angles of a triangle is 180°

∠B + ∠D + ∠BCD = 180° [ Interior Angles ]

∠B + 100° + 30° = 180°

∠B + 130° = 180°

∠B = 180° - 130°

∠B = 50°

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∠ADE

We know that,

Measure of all corresponding angles is equal

∠ADE = ∠B [ Corresponding Angles ]

∠ADE = 50°

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∠EDC

We know that,

Sum of all linear pairs is 180°

∠ADE + ∠EDC + ∠D = 180° [ Linear Pair ]

50° + ∠EDC + 100° = 180°

150° + ∠EDC = 180°

∠EDC = 180° - 150°

∠EDC = 30°

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∠AED

We know that,

Sum of all interior angles of a triangle is 180°

∠A + ∠AED + ∠ADE = 180° [ Interior Angles ]

50° + ∠AED + 50° = 180°

100° + ∠AED = 180°

∠AED = 180° - 100°

∠AED = 80°

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∠ACB

We know that,

Sum of all interior angles of a triangle is 180°

∠A + ∠B + ∠ACB = 180° [ Interior Angles ]

50° + 50° + ∠ACB = 180°

100° + ∠ACB = 180°

∠ACB = 180° - 100°

∠ACB = 80°

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a) ∠EDC = 30°

b) ∠ADE = 50°

c) ∠B = 50°

d) ∠AED = 80°

e) ∠ACB = 80°