Question

the angles of triangle are in A.P. the greatest angle is twice the smallest angle find all angles of triangle​

Answer 1

Answer:

Let the smallest angle be x and other also

thn bigger will be 2 x

2 x +x+x=180

4x =180

180/4=45

x=45

other x will also be 45 and

2x will be 90

.so the angles are 45,45 and 90

Answer 2

Aɴꜱᴡᴇʀ

$\huge \sf{}the \: angles = 40°\:,60°\:,80°\:$

_________________

Gɪᴠᴇɴ

All angles of ∆ are in A.P.

Greatest angle = 2 × least angle.

_________________

ᴛᴏ ꜰɪɴᴅ ᴛᴏ ᴘʀᴏᴠᴇ

All the angles of ∆

_________________

Sᴛᴇᴘꜱ

As angles are in A.P. then let the angles be (a - d), a & (a + d)

Here, least angle = (a - d)° & greatest angle = (a + d)°

As we know,

☛ Sum of 3 angles of ∆ = 180°

A/q,

→ (a + d) = 2(a - d)

→ a + d = 2a - 2d

→ a - 2a = -2d - d

→ -a = -3d

→ a = 3d ------ Equation (1)

Case 2:-

→ (a - d) + a + (a + d) = 180°

→ a - d + a + a + d = 180°

→ 3a = 180°

→ 3(3d) = 180°

→ 9d = 180°

→ d = 180/9

→ d = 20

So, commom difference (d) = 20

Now ,put this value in (Equation 1)

→ a = 3(20)

→ a = 60

Now all angles of ∆ : —

→ First angle = a - d

→ First angle = (60 - 20)°

→ First angle = 40°

→ Second angle = a

→ Second angle = 60°

→ Third angle = (a + d)

→ Third angle = (60 + 20)°

→ Third angle = 80°

Therefore,

All angles of triangle are : 40°,60° & 80° .

_________________

$\huge{\mathfrak{\purple{hope\; it \;helps}}}$