Question

An exterior angle of a triangle is 105 ° . If one of the interior opposite angles is 35 ° , find the other two angles of a triangle.

Answer 1

Step-by-step explanation:

EXTERIOR ANGLE OF THE TRIANGLE= 105 DEGREES

AND BOTH the Interior angles are equal..

let both the equal angles be x degree each

then ,

=> 105° = x°+x°   ∵(exterior angle of a triangle is equal to the sum of interior opposite angles..)

∴ 105° = 2x°

105/2 = x°

therefore,

x° = 52.5°

Answer 2

Answer:

70° and 75°

Step-by-step explanation:

here,

let the one interior be x

35°+ x = 105° (∵ sum of 2 interior angle of a triangle is equals to one exterior angle)

or, x= 105°- 35°

∴ x = 70°

now, let the another angle of the triangle be y

x + 35°+ y = 180° {∵ sum of all interior angle of a triangle is 180°}

or, 70°+ 35°+ y = 180° { ∵ putting value of x}

or, 105° + y = 180°

or, y= 180°- 105°

∴ y = 75°