If ABC is a triangle such that AB - BC and - B-60- then find the measure of - A-

Given, AB = BC ∠ B = 60^∘ Now, ∠ A = ∠ C .. (i) [Angles opposite to equal sides are always equal] In Δ ABC, nbsp; ∠ A + ∠ B + ∠ C=180^∘ [Angle Sum Property] ...

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Standard VI

Mathematics

Lines in a Triangle

If ABC is a t...

Question

If ABC is a triangle such that AB = BC and $∠ B = 60^{\circ}$ , then find the measure of $∠ A$ .

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Solution

Given,
AB = BC
$∠ B = 60^{\circ}$
Now,
$∠ A = ∠ C$ .. (i)
[Angles opposite to equal sides are always equal]

In $Δ$ ABC,
$∠ A + ∠ B + ∠ C = 180^{\circ}$
[Angle Sum Property]
$2 ∠ A + 60^{\circ} = 180^{\circ}$ [From (i)]
$2 ∠ A = 120^{\circ}$
$∠ A = 60^{\circ}$

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If ABC is a triangle such that AB = BC and ∠B=60∘, then find the measure of ∠A.

Given, AB = BC ∠B=60∘ Now, ∠A=∠C .. (i) [Angles opposite to equal sides are always equal] In Δ ABC, ∠A+∠B+∠C=180∘ [Angle Sum Property] 2∠A+60∘=180∘ [From (i)] 2∠A=120∘ ∠A=60∘

If ABC is a triangle such that AB = BC and $∠ B = 60^{\circ}$ , then find the measure of $∠ A$ .

Given,
AB = BC
$∠ B = 60^{\circ}$
Now,
$∠ A = ∠ C$ .. (i)
[Angles opposite to equal sides are always equal]

In $Δ$ ABC,
$∠ A + ∠ B + ∠ C = 180^{\circ}$
[Angle Sum Property]
$2 ∠ A + 60^{\circ} = 180^{\circ}$ [From (i)]
$2 ∠ A = 120^{\circ}$
$∠ A = 60^{\circ}$