Question

Two angles of a triangle are of equal measures and each is one - fourth the measures of the third angle. find all the angles of the triangle.

Answer 1

let third be x
then
first = second = x/4
now by angle sum property of triangle
$\frac{x}{4} + \frac{x}{4} + x = 180 \\ \frac{x}{4} + \frac{x}{4} + \frac{4x}{4} = 180 \\ \frac{6x}{4} = 180 \\ x = 180 \times \frac{4}{6 } \\ x = 120$
now first = second =
$\frac{x}{4} = \frac{120}{4} = 30$
so angles are
30° , 30° , 120°

Answer 2

Answer:

Let the given triangle be DEF.

Angle D= angle E= x°

Then, F=(4x) °

Now, D+E+F= 180°

(Sum of three angles of a triangle is 180°)

So, x+ x + 4x=180°

6x=180°

x=180°/6

x=30°

Hence, ∆D=Angle E = x°=30°

And, angle F=(4x°) =(4*30°)

=120° ans..

Step-by-step explanation:

Thanks