Question

60"FMostly cloudyQuestionThe measure of one angle of a right triangle is 40° more than the measure of the smallest angle. Find the measure of thesmallest angle.Provide your answer below:FEEDBACKMORE INSTRUCTIONSUBMITContent attribution

Answer 1

Recall that the two acute angles of a right triangle add up to 90 degrees.

Let s be the measure (in degrees) of the smallest angle of the given right triangle, then we can set the following equation:

$s+40+s=90.$

Adding like terms we get:

$2s+40=90.$

Subtracting 40 from the above result we get:

$\begin{gathered} 2s+40-40=90-40, \\ 2s=50. \end{gathered}$

Dividing the above result by 2 we get:

$\begin{gathered} \frac{2s}{2}=\frac{50}{2}, \\ s=25. \end{gathered}$

Therefore the measure of the smallest angle is 25º.

Answer: 25º.