Quantitative Aptitude Ques 2233

Question: The measures of two angles of a triangle is in the ratio 4: 5. If the sum of these two measures is equal to the measure of the third angle. Find the smallest angle.

Options:

A) $ 90{}^\circ $

B) $ 50{}^\circ $

C) $ 10{}^\circ $

D) $ 40{}^\circ $

Show Answer

Answer:

Correct Answer: D

Solution:

  • Let the two angles of a triangles be $ 4x $ and $ 5x, $ respectively. Given, third angle = Sum of these two angles. Third angle $ =4x+5x=9x $ Sum of the measure of all the angles of a triangle is $ 180{}^\circ . $

$ \therefore $ $ 4x+5x+9x=180{}^\circ $
$ \Rightarrow $ $ 18x=180{}^\circ $
$ \Rightarrow $ $ x=10{}^\circ $

$ \therefore $ Smallest angle $ =4x=4\times 10=40{}^\circ $

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