In a right triangle, the acute angles measure x + 15 and 2x degrees. What is the measure of the smallest angle of the triangle?
15
25
40
50

Question

In a right triangle, the acute angles measure x + 15 and 2x degrees. What is the measure of the smallest angle of the triangle?
15
25
40
50

parthkohli · Answer

One angle is 90 degrees we know for sure(right triangle)
they add up to 180 degrees.

$\Large \color{MidnightBlue}{\Rightarrow 90 + x + 15 + 2x= 180 }$
$\Large \color{MidnightBlue}{\Rightarrow 105 + 3x = 180 }$
$\Large \color{MidnightBlue}{\Rightarrow 3x = 75 }$
$\Large \color{MidnightBlue}{\Rightarrow x = 25 }$

One angle is x + 15 = 25 + 15 = 40
Second one is 2x = 2*25 = 50
Which is the smaller one?

anonymous · Answer

40