One of the angles of a quadrilateral is 84°. If the ratio of the remaining angles of a quadrilateral is 4:3:5, respectively, then find the difference between the smallest and largest angles.
Show answer & explanation
Correct answer: C
Explanation
Given:
One angle = 84°
Ratio of the other three angles = 4 : 3 : 5
By the formula:
Sum of all angles of a quadrilateral = 360°
Let the other three angles = 4x, 3x, 5x
84 + 4x + 3x + 5x = 360
84 + 12x = 360
12x = 276
x = 23
4x = 92°
3x = 69°
5x = 115°
Smallest angle = 69°
Largest angle = 115°
Difference = 115 − 69 = 46°