Question
The interior angles of a triangle are in the ratio 1 : 2 : 3, then the ratio of its exterior angles is 3 : 2 : 1.
The interior angles of a triangle are in the ratio 1 : 2 : 3, then the ratio of its exterior angles is 3 : 2 : 1.
Answer:
:
False
Given, the ratio of interior angles = 1 : 2 : 3.
Let the interior angles be x, 2x and 3x.
So, x+2x+3x=180∘ [angle sum property of triangle]
⇒6x=180∘⇒x=180∘6=30∘
∴ The interior angles are 30∘,60∘ and 90∘.
Now, the exterior angles will be (180∘−30∘),(180∘−60∘) and (180∘−90∘)
i.e. 150∘,120∘ and 90∘.
The ratio of exterior angles =150∘:120∘:90∘=15:12:9=5:4:3.
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:
False
Given, the ratio of interior angles = 1 : 2 : 3.
Let the interior angles be x, 2x and 3x.
So, x+2x+3x=180∘ [angle sum property of triangle]
⇒6x=180∘⇒x=180∘6=30∘
∴ The interior angles are 30∘,60∘ and 90∘.
Now, the exterior angles will be (180∘−30∘),(180∘−60∘) and (180∘−90∘)
i.e. 150∘,120∘ and 90∘.
The ratio of exterior angles =150∘:120∘:90∘=15:12:9=5:4:3.
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