Question

In the figure given, what are the values of angle b, angle c and angle a respectively?
(A). 18°, 70° and 92°
(B).92º, 70° and 18°
(C). 70°, 92° and 18°
(D), 70°, 18° and 92°​

Answer 1

Answer:

Option (A) is correct.

Step-by-step explanation:

To find:-

The values of ∠a, ∠b and ∠c.

According to the question,

In the figure, it is given that

∠ADB = 35°, ∠AEC = 46°, AB = BD and AC = CE

Now,

In ΔACE,

Since AC = CE

⇒ ∠AEC = ∠EAC (Angles opposite to equal sides are equal)

⇒ 46° = ∠EAC

⇒ ∠EAC = 46°

So,

∠c = ∠AEC $+$ ∠EAC (Exterior angle property)

∠c = 46° + 46°

∠c = 92°

Similarly,

In ΔABD,

Since AB = BD

⇒ ∠ADB = ∠DAB (Angles opposite to equal sides are equal)

⇒ 35° = ∠DAB

⇒ ∠DAB = 35°

So,

∠b = ∠ADB $+$ ∠DAB (Exterior angle property)

∠b = 35° + 35°

∠b = 70°

Now,

In ΔABC,

∠a $+$ ∠b $+$ ∠c $=$ 180° (Angle sum property)

∠a + 70° + 92° = 180°

∠a = 180° - 162°

∠a = 18°

Final answer: Option (A) is correct.

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