Question

2. In the figure given, what are the values of La? А a (35° 46° bº B cº D С C E (a) 92 (c) 20° (b) 18° (d) 15°​

Answer 1

Answer:

18 is the answer

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Answer 2

• ∠a is equal to 18° .

To Find :- In the figure given, what are the values of ∠a ?

(a) 92° (b) 20° (c) 18° (d) 15°

Concept used :-

• Sum of all three angles of a triangle is equal to 180° .
• Angle opposite to equal sides of a triangle are equal in measure .
• Exterior angle of a traingle is equal to sum of opposite interior angles .

Solution :-

In ∆ABD,

→ AB = BD

So,

→ ∠ADB = ∠DAB { Angle opposite to equal sides of a triangle are equal in measure . }

then,

→ ∠ABC = ∠ADB + ∠DAB { Exterior angle is equal to sum of opposite interior angles . }

→ ∠ABC = 35° + 35°

→ ∠ABC = 70°

→ ∠b = 70° -------- Equation (1)

Similarly,

In ∆ACE,

→ AC = CE

So,

→ ∠AEC = ∠CAE { Angle opposite to equal sides of a triangle are equal in measure . }

then,

→ ∠ACB = ∠AEC + ∠CAE { Exterior angle is equal to sum of opposite interior angles . }

→ ∠ACB = 46° + 46°

→ ∠ACB = 92°

→ ∠c = 92° --------- Equation (2)

Now in ∆ABC,

→ ∠ABC + ∠ACB + ∠CAB = 180° { Angle sum property of a triangle }

→ ∠b + ∠c + ∠a = 180°

putting values from Equation (1) and (2),

→ 70° + 92° + ∠a = 180°

→ 162° + ∠a = 180°

→ ∠a = 180° - 162°

→ ∠a = 18° (Ans.)

Hence, Option (c) 18° is correct answer .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

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