Question

In ΔABC, if m∠A = m∠B/2 = m∠C/3, then find the measures of all the angles of ΔABC.

Answer 1

Take,angle A=x
Then B=2x
C=3x
By angle sum property
A+B+C=180
x+2x+3x=180
6x=180
x=180/6
x=30=A
B=2x=60
C=3x=90
I hope this is help full

Answer 2

Step-by-step explanation:

Explanation:

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$\bf{QUESTION - }$

In a ΔABC , ∠C = 3∠B = 2(∠ A + ∠ B ) . Find the angles .

→ let ∠a = x° and ∠b = y°

Then

∠C= 3∠B= 3(y°)

Now,

→ ∠C = 2(∠A+∠B)

=> 3y = 2(x+y)

=> 2x - y = 0............(1)

we know that the sum of angles of triangle is 180°

.°. ∠A + ∠B + ∠C = 180°

=> x + y + 3y = 180

=> x + 4y = 180...........(2)

on multiplying (1) by 4 and adding result with (2), we get

8x + x = 180

= 9x = 180

=> x = 180/9

=> x = 20

putting x = 20 in equation (1)

we get

→ y=(2×20)

→ y=40

thus,

x=20

y=40

Hence

→ ∠a = 20°

→ ∠a = 20° → ∠b=40°

$\sf{ \angle \: c = (3 \times 40) = \: 120 \degree}$