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Difficulty: EasyPolygon Angles and Properties

The interior angles of a quadrilateral are in the ratio 2:3:4:62:3:4:6. What is the degree measure of the largest interior angle of the quadrilateral?

  1. A
    4
  2. B
    48
  3. C
    72
  4. 144Answer
  5. E
    240

Answer

144
The sum of the interior angles of a quadrilateral is 360∘360^\circ. Given the ratio 2:3:4:62:3:4:6, the sum of the parts is 2+3+4+6=152 + 3 + 4 + 6 = 15. The value of one part is 360∘÷15=24∘360^\circ \div 15 = 24^\circ. The largest angle corresponds to the largest part of the ratio, which is 66. Therefore, the largest angle measure is 6×24∘=144∘6 \times 24^\circ = 144^\circ.

Step-by-Step Solution

1
Determine the sum of the interior angles of a quadrilateral.
The sum of the interior angles of any quadrilateral is 360∘360^\circ.
This is a fundamental property of quadrilaterals, which can also be derived using the formula (n−2)×180∘(n - 2) \times 180^\circ with n=4n = 4.
2
Calculate the total number of parts in the given ratio.
The sum of the ratio parts is 2+3+4+6=152 + 3 + 4 + 6 = 15.
Adding the parts of the ratio allows us to find the size of a single share of the total angle sum.
3
Find the measure of one part of the ratio.
One part is equal to 360∘÷15=24∘360^\circ \div 15 = 24^\circ.
Dividing the total sum of the angles by the sum of the ratio parts determines the angle measure per ratio unit.
4
Multiply the largest ratio part by the value of one part to find the largest angle.
The largest angle is 6×24∘=144∘6 \times 24^\circ = 144^\circ.
The largest interior angle corresponds to the largest number in the ratio, which is 66.

Key Concept

Using ratios to find angle measures in a polygon.
Estimated Time:45s
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Topics

Polygon Angles and Properties

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