Question

1. The value of x in the given figure is.
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Answer 1

Answer:

in triangle ABC,

angle A=35°

angle B=30°

so angle C=180-(35+30)°=(180-65)°=115°

angle DCE=(180-115)°=65°

external angle x=two distance interior angle

=(65+35)°=100°

so value of x=100°

Answer 2

Given

• In ∆ ABC, ∠BAC = 35° and ∠ABC = 30°
• In ∆ DEC, ∠DEC = 35°

To Find

• Measure of ∠BDE (x) = ?

Solution

• In ∆ ABC

➵ ∠A + ∠B + ∠BCA = 180° (A S.P)

➵ 35° + 30° + ∠BCA = 180°

➵ 65° + ∠BCA = 180°

➵ ∠BCA = 180° - 65°

➵ ∠BCA = 115°

Also

➵ ∠BCA + ∠BCE = 180° (L.P)

➵ 115° + ∠BCE = 180°

➵ ∠BCE = 180° - 115°

➵ ∠BCE = 65°

☯〘We can also write ∠BCE as ∠DCE)〙

Now

• In ∆ DEC

➵ ∠CDE + ∠DCE + ∠DEC = 180° (A.S.A)

➵ ∠CDE + 65° + 35° = 180°

➵ ∠CDE + 100° = 180° $\:$

➵ ∠CDE = 180° - 100°

➵ ∠CDE = 80°

Also

➵ ∠BDE + ∠CDE = 180° (L.P)

➵ x + 80° = 180°

➵ x = 180° - 80°

➵ x = 100°

∴ Hence, value of 'x' is 100°

Note

• '(A.S.A)' and '(L.P)' stands for "Angle Sum Property" and "Linear Pair"!

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