Question

In ΔABC, ∠A : ∠B : ∠C = 1 : 2 : 3. Find the angles and identify the type of the triangle.

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Answer 1

$∠A:∠B:∠C=1:2:3$

$</p><p>∠A=x, \: ∠B=2x \: and∠C=3x$

$∠A+∠B+∠C=180∘$

$⇒x+2x+3x=180∘$

$⇒x=180∘ \div 6=30∘$

$∠A=30∘,∠B=60∘and∠C=90∘$

Answer 2

Answer:

${\boxed{\orange{\underline{\text{∠A=30°,∠B=60°and∠C=90°}}}}}$

Explanation:

In ΔABC,∠A:∠B:∠C=1:2:3 <GIVEN>

${\red{\text{Let, ∠A=x, ∠B=2x and ∠C=3x. -->[1]}}}$

${\pink{\text{We know, Sum of all Angles of a Triangle is 180°}}}$

Therefore, ∠A+∠B+∠C=180°

⇒ x + 2x + 3x = 180°

⇒ x = 180° ÷ 6

⇒ x = 30°

${\green{\text{Put the Value of "x" in equation no.[1], We get}}}$

∠A=30°,∠B=60°and∠C=90°