Question

16. The measures of the acute angles of a right triangle have a ratio of 2 :7.

What is the measure of the smaller angle?

Answer 1

The smaller angle is 20 degrees.

Explanation:

A triangle's interior angles must have a sum of 180 degrees. Hence the two acute angles must have a sum of 180-90=90 degrees.

Say that the angles have 2x and 7x length:

2x+7x=90

9x=90

x=10

Hence the acute angles have degrees 2*10=20, 7*10=70.

The smaller angle is 20 degrees.

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