Question

The value of ‘x’ if ∠ = 35 degree, ∠B= 60degree and ∠ = 20degree is:

Answer 1

Answer:- x= 115°

Hope this answer helps you !

Answer 2

∵The sum of the measure of all angles of triangle is 180° .

$In \: ∆ABC, \\ \\ \therefore \: \angle \: CAB \: + \angle \: ABC + \angle \: BCA \: = 180 \degree \\ \therefore \: 35 \degree \: + 60 \degree + \angle \: BCA = 180 \degree \\ \therefore \: 95 \degree + \angle \: BCA \: = 180 \degree \\ \therefore \angle \: BCA \: = 180 \degree \: - 95 \degree \\ \therefore \boxed {\: \angle \: BCA = 85 \degree}$

$In \: ∆ABC \: and \: ∆CDE , \\ \\ \therefore \angle \: BCA + \angle \: ECD \: = 180 \degree \\ - ( Angles \: in \: linear \: pair ) \\ \therefore \: 85 \degree + \angle \: ECD \: = 180 \degree \\ \therefore \angle \: ECD \: = 180 \degree - 85 \degree \\ \therefore \boxed { \angle \: ECD \: = 95 \degree}$

Theorem : The measure of an exterior angle of a triangle is equal to the sum of its remote interior angles.

$\angle \: x \: is \: the \: exterior \: angle \: of \: ∆ CDE \\ \therefore \angle \: ECD + \angle \: EDC \: = \angle \: x \\ \therefore \: 95 \degree \: + 20 \degree \: = \angle \: x \\ \therefore \boxed{\angle \: x \: = 115 \degree}$

Option (iii) 115° is Correct.