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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.

Respuesta :

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=[tex]\frac{1}{4}[/tex] x

Largest angle= 5 x- 20°

A T Q

x+ [tex]\frac{1}{4}[/tex] x + 5x-20= 180°

[tex]\frac{4x+x+20x}{4}[/tex] = 180+ 20

[tex]\frac{25x}{4}[/tex] = 200

x= [tex]\frac{200}{25}[/tex] × 4

x= 32°'

Smallest angle is 32°

Hence, the smallest angle is [tex]\frac{1}{4}[/tex] x= [tex]\frac{1}{4}[/tex]×32°= 8°

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

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