Question

The interior angle of a traingle are in the ratio 1:2:3. Find the ratio of its exterior angles.
in the book on the last page answer is 5:3:4​

Answer 1

Step-by-step explanation:

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. Ratio of its exterior angles : 150 : 120 : 90 Dividing by 30°

Answer 2

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

\begin{gathered}\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}}}}\end{gathered}⟶1x+2x+3x=180∘⟶6x=180∘⟶x=6180⟶x=30∘

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\begin{gathered}\longrightarrow\sf First \ angle = 30^{\circ}\\\\\\\longrightarrow\sf Second \ angle = 30 (2) = 60^{\circ} \\\\\\\longrightarrow\sf Third \ angle = 30 (3) = 90^{\circ}\end{gathered}⟶First angle=30∘⟶Second angle=30(2)=60∘⟶Third angle=30(3)=90∘

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\bigstar★ Exterior Angles are :

\begin{gathered}\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}}\end{gathered}⟶180−30⟶150∘⟶180−60⟶120∘⟶180−90⟶90∘

\begin{gathered}\\\end{gathered}

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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 \: }}}Ratio is 5:4:3