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Question

Difficulty: EasyProperties of Quadrilaterals

The interior angles of a quadrilateral are in the ratio 2:3:3:42:3:3:4. What is the measure, in degrees, of the largest interior angle of this quadrilateral?

  1. A
    60
  2. B
    90
  3. 120Answer
  4. D
    180
  5. E
    240

Answer

120
The correct answer is 120. The sum of the interior angles of any convex quadrilateral is 360 degrees. Given the ratio of the interior angles is 2:3:3:42:3:3:4, the total number of parts is 2+3+3+4=122 + 3 + 3 + 4 = 12. Dividing the total angle sum by the total parts gives the value of one part: 360∘/12=30∘360^\circ / 12 = 30^\circ. The largest angle has 4 parts, so its measure is 4×30∘=120∘4 \times 30^\circ = 120^\circ.

Step-by-Step Solution

1
Calculate the sum of the parts in the given ratio of the angles.
2+3+3+4=122 + 3 + 3 + 4 = 12 parts
To find the fractional share of each angle, we must first determine the total number of equal parts in the ratio.
2
Determine the value in degrees of a single part of the ratio using the sum of interior angles of a quadrilateral.
360∘/12=30∘360^\circ / 12 = 30^\circ per part
The sum of the interior angles of any convex quadrilateral is 360 degrees. Dividing this sum by the total number of parts gives the angle measure of one part.
3
Multiply the value of one part by the number of parts of the largest angle.
4×30∘=120∘4 \times 30^\circ = 120^\circ
The largest angle corresponds to the largest number in the ratio, which is 4.

Key Concept

Sum of interior angles of a quadrilateral and ratio distribution
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Topics

Properties of Quadrilaterals

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