Question

I will mark you the brainliest for correct answers plz be fast Please view the image, and respond.

Answer 1

Given :-

Angles of a triangle are ( x - 14° ) , ( 2x - 31° ) , y and exterior angle ( 5x - 155° )

To Find :-

Value of "x" , "y" and the property used and the property used .

Used Concepts :-

• Exterior angle property which states that the exterior angle is equal to the sum of the angles opposite to the interior angle with the given exterior angle .
• Angle Sum Property of triangle which states that the sum of all interior angles of a triangle is 180° .

Solution :-

Let's say the triangle be ∆ ABC ,

Again , Let ,. ∠1 = ( x - 14° )

∠2 = ( 2x - 31° )

∠3 = y

∠4 = ( 5x - 155° )

Then ,.By Exterior Angle Property of Triangle ,

∠1 + ∠2 = ∠4

=> ( x - 14° ) + ( 2x - 31° ) = ( 5x - 155° )

=> x - 14° + 2x - 31° = 5x - 155°

=> x + 2x - 5x = -155° + 31° + 14°

=> -2x = - 155° + 45°

=> -2x = -110°

=> x = -110°/-2

=> x = 55°

Now , By Angle Sum Property of Triangle ,

∠1 + ∠2 + ∠3 = 180°

=> ( x - 14° ) + ( 2x - 31° ) + y = 180°

=> ( 55° - 14° ) + ( 2 × 55° - 31° ) + y = 180°

=> 41° + ( 110° - 31° ) + y = 180°

=> 41° + 110° - 31° + y = 180°

=> 120° + y = 180°

=> y = 180° - 120°

=> y = 60°

∠1 = x - 14° = 55° - 14° = 41°

∠2 = 2x - 31° = 2 × 55° - 31° = 110° - 31° = 79°

∠3 = y = 60°

∠4 = 5x - 155° = 5 × 55° - 155° = 275° - 155° = 120°

Henceforth , y = 60° and x = 55° and the property used is Angle Sum Property of Triangle and Exterior Angle Property .