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den301095 [7]
3 years ago
13

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.
Mathematics
1 answer:
vivado [14]3 years ago
6 0

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°

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