Question

Three angles of a triangle are in the ratio 1:2:1. Find all the angles of the triangle. Classify the triangle in two different ways​

Answer 1

Answer:

Let it be Triangle ABC

Let,

∠A = x

∠B = 2x

∠C = x

• As we know measures of all angles of triangle is 180°

So,

x + 2x + x = 180°

$\implies$ 4x = 180

$\implies$ x = $\dfrac{180}{4}$

$\implies$ x = $\boxed{\sf{45°}}$

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∠A = 45 × 1 = 45 °

∠B = 45 × 2 = 90°

∠C = 45 × 1 = 45°

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Since ∠A = ∠C

ABC is isosceles Traingle

Since ∠B = 90

ABC is Right angled at B.

$\bf{\red{Hope \: it \: helps \: uh!}}$

Answer 2

❍ Let the angles of the traingle be x, 2x and x respectively.

$\underline{\pink{\bigstar\:\boldsymbol{By\: Using\; ASP \; Property\::}}}$⠀⠀

• Angle Sum Property of Triangle is basically, sum of all angles of the triangle is 180°.

Therefore,

$\dashrightarrow\sf x + 2x + x = 180^\circ \\\\\\\dashrightarrow\sf 2x + 2x = 180^\circ \\\\\\\dashrightarrow\sf 4x = 180^\circ \\\\\\\dashrightarrow\sf x = \cancel\dfrac{180^\circ}{4} \\\\\\\dashrightarrow{\underline{\boxed{\frak{\pink{x = 45^\circ}}}}}$

Hence,

• First angle, x = 45°
• Second angle, x = 45°
• Third angle, 2x = 2(45)° = 90°

$\therefore{\underline{\sf{Hence,\;angles\;of\;the\;\triangle\;are\; \bf{45^\circ,90^\circ\;\&\;45^\circ}.}}}$

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C L A S S I F Y I N G :

• Here, we can see that Triangle has two equal angles, (45° and 45°). Therefore, the triangle is an isosceles triangle. (Isosceles triangle has two equal angles).

• And, In the given triangle one angle is equal to 90° also. Therefore, the triangle is right – angled triangle.