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A day full of math games & activities. Find one near you.
The measures of the angles of a triangle are in the extended ratio 2: 2: 8. What is the measure of the smallest angle?
A triangle is a polygon with three sides, three angles, and three vertices. The sum of interior angles of a triangle is 180º.
Answer: For the angles of a triangle given in the ratio 2: 2: 8, the measure of the smallest angle of the triangle is 30º.
Let us find the smallest angle of this triangle.
Explanation:
Given that the angles of a triangle are in the ratio of 2: 2: 8.
Let the angles be 2x, 2x, and 8x.
By angle sum property of triangle,
⇒ 2 x + 2 x + 8x = 180º
⇒ 12 x = 180º
⇒ x = 180º / 12
⇒ x = 15º
The measures of the angles are:
2x = 2 × 15º = 30º
2x = 2 × 15º = 30º
8x = 8 × 15º = 120º
Thus, the measure of the smallest angle of the triangle is 30º.
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