Question

the interior angles of a triangle are in ratio 1:2:3. find the ratio of its exterior angles.​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

AnswEr

Given: Interior angles of a Traingle are in the ratio of 1:2:3.

• So, Let's consider that the angles of the triangle be 1x, 2x & 3x.

• Using Angle sum property of Triangle

$\longrightarrow\sf 1x + 2x + 3x = 180^{\circ} \\\\\\\longrightarrow\sf 6x = 180^{\circ} \\\\\\\longrightarrow\sf x = \cancel\dfrac{180}{6} \\\\\\\longrightarrow\sf \boxed{\frak{\purple{x = 30^{\circ}}}}$

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$\longrightarrow\sf First \ angle = 30^{\circ}\\\\\\\longrightarrow\sf Second \ angle = 30 (2) = 60^{\circ} \\\\\\\longrightarrow\sf Third \ angle = 30 (3) = 90^{\circ}$

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$\bigstar$ Exterior Angles are :

$\longrightarrow\sf 180 - 30\\\\\\\longrightarrow\sf\pink{150^{\circ}}\\\\\\\longrightarrow\sf 180 - 60\\\\\\\longrightarrow\sf\blue{120^{\circ}}\\\\\\\longrightarrow\sf 180 - 90\\\\\\\longrightarrow\sf\purple{90^{\circ}}$

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$\bigstar$ Ratio of its exterior angles :

150 : 120 : 90 Dividing by 30°

$\qquad\qquad\boxed{\sf{\red{\: Ratio \ is \ 5 : 4 : 3 \: }}}$