Question

The angles of a triangle are in an A.P. The smallest angle is 30o
. Find all the angles of a
triangle.

Answer 1

Answer:

angles of a triangle are in an A.P

$2 {b} = a + c$

$2b = 180 - b$

$b = 60$

$a = 30$

$a + b + c = 180$

$c = 180 - (60 + 30) = 90$

Answer 2

Explanation:

When numbers are in an arithmetic progression, the difference between two consecutive number is a constant value.

Therefore,

Since the smallest angle is 30, we can assume that the common difference between the numbers is 30.

Therefore, the angles are

30 + 30 = 60

30 + 2(30) = 30 + 60 = 90

Verification:

According to the angle sum property of a triangle, sum of all its side is 180 degrees.

30 + 60 + 90 = 180, meaning the angles we found are correct and in AP.

Answer: 30, 60, 90