The angles of a triangle are in the ratio 3:4:5. Find the measure of the smallest angle

overrated3245w

overrated3245w

Answered question

2022-09-08

The angles of a triangle are in the ratio 3:4:5. Find the measure of the smallest angle

Answer & Explanation

Matthew Benton

Matthew Benton

Beginner2022-09-09Added 9 answers

The sum of the interior angles of a triangle will be 180°.
Therefore, think of the ratios of 3:4:5 as variables followed by "x" (3x, 4x, and 5x).
Combine like terms and set the equation equal to 180, the amt. of degrees in a triangle:
123x = 180
Now, divide to isolate for x:
( 180 12 ) = 15 , so x = 15
Now, substitute x for 15 in your variables:
3x, 4x, and 5x
3(15), 4(15), and 5(15)
45, 60, and 75 = 180
Therefore, 45 is the smallest angle.

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