Question

The measure of the angles of a triangle are in AP and the greatest is 5 times the smallest .find the angles in degree and radian

Answer 1

Step-by-step explanation:

MOST IMPORTANT PROPERTY TO BE USED HERE IS THAT THE SUM OF ANGLES OF A TRIANGLE IS 180° .

NOW , considering it to be in A.P . let us assume first angle to be equal to "a" . Then , the third and the largest is 5a . Now , let the second angle be equal to a+d . Using the properties of an AP , we get that , (a+d - a ) = 5a - (a +d)

This gives , d = 4a -d ------ (1)

Also , a + (4a-d) + a + 5a = 180

11a - d = 180 --------- (2)

From 1 , d = 2a .

putting this in 2 .

a = 20 °.

d = 40°

So angles respectively will be 20 ° , 60° and 100° . Now you can convert the same into radians . Hence will be your answer .

HOPE THIS HELPED. .

MARK THE BRAINLIEST PLEASE .

Answer 2

Step-by-step explanation:

Angles are in A.P. Let the angles of the triangle be a, a+d, a+2d

Sum of three angles is equal to 180.

a+a+d+a+2d=180

3a+3d=180

a+d=60 ——(1)

Smallest angle = a ; Greatest angle= a+2d

a+2d=5a

d=2a

From (1), a+2a=60

a=20

d=2(20)=40

Ans: The angles 20°, 60° and 100°. In radians π/9, π/3 , 5π/9