5. Three angles of a quadrilateral are in the
ratio 3: 4:5. The difference of the least
and the greatest of these angles is 45°. Find
all the four angles of the quadrilateral.
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1
Answer:
67.5°, 90°, 112.5°, 90°
Step-by-step explanation:
The three angles are 3x, 4x, 5x
Difference b/w greatest and least angle =45°
5x - 3x = 45
x = 22.5°
So, the angles are
3x = 3×22.5 = 67.5°
4x = 4×22.5 = 90°
5x = 5×22.5 = 112.5°
The fourth angle = 360 - (67.5+90+112.5) ∵ [Sum of four interior angles of quadrilateral is 360°]
= 90°
The all four angles = 67.5°, 90°, 112.5°, 90°
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