Question

one side of a triangle is produced and the exterior angle so formed is 120° . If the interior opposite angles are in the ratio 2:3,find the measure of the triangle​

Answer 1

Answer:

Let the measure angles of triangle be 'x'

Therefore, 2x+ 3x = 120° (property of remote interior angle)

5x = 120°

x= 120/5

x= 24°

therefore 2x = 2(24)

= 48°

3x = 3 (24)

= 72°

Therefore, 48+72+ angle = 180°

120 + angle = 180°

angle = 180 - 120

= 60°

Therefore, angles of triangles = 48°, 72°, 60°

Answer 2

Answer:

60°,48°and 72°

Step-by-step explanation:

given:

the exterior angle = 120°

the interior opposite angles are in a ratio = 2:3

to find :

measure of triangle

let the interior angles of triangle X,Y,and Z

and exterior angle is P

1. X+P=180°

P=120°

so,X=120°-180°

=60°

2.and another interior angles are in a 2:3 ratio

the left measurement =60°-180°

=120°

the value of ratio = total measurements ÷ sum of ratios

so,the value of 2:3=120°÷(2+3)

120°÷5=24

• the value of Y = 24×2=48
• and the value of Z=24×3=72

we found all measurements of triangle