Question

in the given figure find the measure of angle C A B is 85 degree c is 118 degree is 2 x + 5 degree​

Answer 1

$\underline{\Huge\mathfrak{Answer-}}$

Given ;

Angle B = 85°
Angle A = (2x + 5)°

Assuming a line segment between angle D and angle B.

Than ,
We know that , the sum of the angles on a line is 180°.

So ,

=> 180° - 118° = Angle C

=> Angle C = 180° - 118°

=> Angle C = 62°

Hence , Angle C = 62°

Now , Finding the measure of angle CAD ;-

We know that , Sum of all the angles of a triangle are 180°.

So ,

=> 62° + 85° + (2x + 5)° = 180°

=> 62° + 85° + 2x + 5° = 180°

=> 147° + 2x + 5° = 180°

=> 2x + 5° = 180° - 147°

=> 2x + 5° = 33°

=> 2x = 33° - 5°

=> 2x = 28°

=> x = 28/2 = 14°

Therefore ,
Angle CAD = 33°

Answer 2

angle A =85

angle C =118=2x+5

A+C= 118

85+2x+5=118

90+2x=118

2x=118-90

2x= 28

x=14

therefore, Angle C = 2x+5

=2×14+5

=28+5

= 33