Question

The sum of the measures of the angles of a triangle is 180 degrees°. The smallest angle of the triangle has a measure one fourth 1 4 the measure of the second smallest angle. The largest angle has a measure that is 2020 degrees° less than 55 times the measure of the second smallest angle. Determine the measure of each angle.

Answer 1

Answer:

8°,32°,140°.

Step-by-step explanation:

Sum of measure of angles of a triangle is 180°

Let the second smallest angle be x°

Smallest angle=$\frac{1}{4}$ x

Largest angle= 5 x- 20°

A T Q

x+ $\frac{1}{4}$ x + 5x-20= 180°

$\frac{4x+x+20x}{4}$ = 180+ 20

$\frac{25x}{4}$ = 200

x= $\frac{200}{25}$ × 4

x= 32°'

Smallest angle is 32°

Hence, the smallest angle is $\frac{1}{4}$ x= $\frac{1}{4}$×32°= 8°

Largest angle is 5x- 20= 5×32- 20= 140°