Question

the measures of angles of a triangle are in an AP. the greatest angle is 5 times the smallest. find all the angles in degrees and radians​

Answer 1

Answer:

Please find attachment

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Answer 2

Answer:

The angles in degrees are 20° , 60°, 100°.

Angles in radians $\frac{22}{63} ,\frac{66}{63} ,\frac{110}{63}$.

Step-by-step explanation:

Sum of angles of a triangle = 180

Smallest angle = x

Largest angle = 5x

Given that the angles are in A.P

Third angle =$\frac{x+5x}{2} =\frac{6x}{2} =3x$

Hence, x + 3x + 5x = 180

9x = 180

x = 20°

And 3x = 3(20) = 60°

5x = 5(20) = 100°

In Radians

20 = $\frac{22}{7} *\frac{20}{180} =\frac{22}{63}$

60 = $\frac{22}{7}*\frac{60}{180} =\frac{66}{63}$

100 = $\frac{22}{7} *\frac{100}{180} =\frac{110}{63}$

Therefore, the angles in degrees are 20° , 60°, 100°.

Angles in radians $\frac{22}{63} ,\frac{66}{63} ,\frac{110}{63}$.