Question

21. Find the value of x.
(a) 70°
(b) 75°
(c) 60°
(d) 65°​

Answer 1

Answer :-

• Value of x is 70°.

Given :-

• A triangle with two exterior angles.

To Find :-

• Value of x

Solution :-

[ REFER TO THE ATTACHMENT ]

⇒ ∠ABD + ∠ABC = 180° [ linear pair ]

⇒ 130° + ∠ABC = 180°

⇒ ∠ABC = 180° - 130°

⇒ ∠ABC = 50°

⇒ ∠ACE + ∠ACB = 180° [ linear pair ]

⇒ 125° + ∠ACB = 180°

⇒ ∠ACB = 180° - 125°

⇒ ∠ACB = 55°

In ∆ABC

⇒ ∠ABC + ∠ACB + ∠CAB = 180° [ angle sum property of a triangle ]

⇒ 50° + 55° + x = 180°

⇒ 110° + x = 180°

⇒ x = 180° - 110°

⇒ x = 70°

Verification :-

⇒ ∠ABC + ∠ACB + ∠CAB = 180°

⇒ 50° + 55° + 70° = 180°

⇒ 110° + 70° = 180°

⇒ 180° = 180°

Hence, verified !

Answer 2

ANSWER :

• Value of x is 75°

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Given :

• $\angle$ ABC = 130°

• $\angle$ EDC = 125°

To Find :

• Value of x

Solution :

• Sum of linear pair is 180°

→ $\angle$ ABC + $\angle$ CBD = 180°

→ $\angle$ 130° + $\angle$ CBD = 180°

→ $\angle$ CBD = 180° - 130°

→ $\angle$ CBD = 50°

• Now , as we know , measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles

→ $\angle$ CDE = $\angle$ CBD + $\angle$ x

→ $\angle$ 125° = 50° + $\angle$ x

→ $\angle$ x = 125° - 50°

→ $\angle$ x = 75°

___________________________

• Verification :

• Angle sum property of a ∆ is 180°

→ $\angle$ CBD + $\angle$ x + $\angle$ CDB = 180°

→ 50° + 75° + 55° = 180°

→ 180° = 180°

• LHS = RHS , hence verified .

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