Question

In the figure given below, measures of some angles are indicated. Find the value of x.​

Answer 1

Answer:

Given: ∠DAE=30

∘

,DFC=60

∘

,∠FEG=120

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To find: ∠FCH=x

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Solution: Clearly, ∠AED+∠FEG=180

∘

[Linear pair]

⇒∠AED+120

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=180

∘

⇒∠AED=180

∘

−120

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⇒∠AED=60

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Now, △AED by angle sum property of triangle, we have

∠ADE+∠AED+∠DAE=180

∘

⇒∠ADE+60

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+30

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=180

∘

⇒∠ADE=180

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−60

∘

−30

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⇒∠ADE=90

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Again clearly, ∠ADE+∠FDC=180

∘

[Linear pair]

⇒90

∘

+∠FDC=180

∘

⇒∠FDC=180

∘

−90

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⇒∠FDC=90

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Again, in △FDC by angle sum property of triangle, we have

∠FDC+∠DFC+∠FCD=180

∘

⇒90

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+60

∘

+∠FCD=180

∘

⇒∠FCD=180

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−90

∘

−60

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⇒∠FCD=30

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Again clearly, ∠FCD+∠FCH=180

∘

[Linear pair]

⇒30

∘

+∠FCH=180

∘

⇒∠FCH=180

∘

−30

∘

⇒∠FCH=150

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Answer 2

ANSWER: 150

STEP-BY-STEP EXPLANTION:

∠DEA = 180° - 120° = 60° (Angle sum property of a triangle)

∠DAE = 30°

In triangle DAE,

∠DAE + ∠DEA + ∠ADE = 180° (Angle sum property of a triangle)

60° + 30° + ∠ADE = 180°

∠ADE = 90°

∠CDF = 180° - ∠ADE (linear pair)

∠CDF = 180° - 90° = 90°

∠CDF = 90°

In triangle CDF,

∠CDF + ∠DFC + ∠DCF = 180°

90° + 60° + ∠DCF = 180°

∠DCF = 180° - 150°

∠DCF = 30°

∠x + ∠DCF = 180° (linear pair)

∠x = 180° - 30°

∠x = 150°

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