Question

Three angles of a triangle are in an arithmetic progression. If the largest angle
is 75 , find the remaining angles.
with method please

Answer 1

Solution;

Let us assume the three angles to be: (a-d), a, (a+d).

It is given that largest angle of the triangle is 75°

According to our assumption, the largest angle is (a+d).

Therefore (a+d) = 75°

Now we know that, according to Angle Sum Property of a triangle, the sum of all the interior angles is equal to 180°. This implies:

→ a - d + a + a + d = 180°

→ 3a = 180°

→ a = 180°/3 = 60°

Now based on our assumption we get:

→ a + d = 75°

→ 60° + d = 75°

→ d = 75° - 60° = 15°

Therefore substituting the values in our assumptions we get:

• a - d ⇒ 60° - 15° = 45°
• a ⇒ 60°
• a + d ⇒ 75°

Therefore the remaining angles are 45° and 60°

Answer 2

$\huge \mathtt{ \fbox{Solution :)}}$

Given ,

• The three angles of triangle are in AP
• The largest angle is 75

Let , the three angles of triangle are (a - d) , a , and (a + d)

We know that ,

The sum of all angles of triangle is 180

Thus ,

a - d + a + a + d = 180

3a = 180

a = 180/3

a = 60

Since , the largest angle is 75

Thus ,

a + d = 75

60 + d = 75 { because , a = 60 }

d = 75 - 60

d = 15

Hence , the three angles are 45 , 60 and 75

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