Question

The exterior angle of a triangle is 50 degree & interior opposite
angle are in the ratio 2:3, find the three angles of the
triangle?​

Answer 1

Answer:

As we know the a theorem that the exterior angle is the sum up of two interior opposite angles so in here this condition 2:3

let this ratio be as 2x and 3x where x is any constant that we gotta find here

then Acc. to theorem 2x + 3x = 50

x=10

then angles will be

2 * 10= 20

3 * 10= 30 and third angle by angle sum property of triangle that sum of all angles is 180 degrees

then third angle is 180 -(20+ 30) = 130 degrees

so angles are 20, 30 and 130 in degree

HOPE IT HELPS

Answer 2

Answer:

20° , 30° , 130°

Step-by-step explanation:

given,

in a triangle,

exterior angle of a triangle = 50°

and given that,

angles opposite to

that exterior angle are in

ratio 2:3

let the common ratio be x

then internal opposite angles will

2x and 3x

we know that,

an exterior angle of a triangle is equal to the sum of two opposite internal angles

so,

according to diagram ,

angle ABC + BAC = BCD

ABC = 2x

BAC = 3x

BCD = 50°

then,

2x + 3x = 50°

5x = 50

x = 50/5

x = 10

now,

angles are

2x = 2(10)

= 20°

3x = 3(10)

= 30°

so,

two angles are 20° and 30°

let the third angle be y

here, y = BCA

then,

by the angle sum theorem of a triangle

sum of angles of a triangle is 180°

so,

ABC + BAC + BCA = 180

20 + 30 + y = 180

50 + y = 180

y = 180 - 50

y = 130°

so,

third angle = 130°

so,

angles of triangle

➡ 20° , 30° , 130°