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.

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= x

Largest angle= 5 x- 20°

A T Q

x+ x + 5x-20= 180°

= 180+ 20

= 200

x= × 4

x= 32°'

Smallest angle is 32°

Hence, the smallest angle is x= ×32°= 8°

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

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°