Question

please solve it correctly
find the value of x???????
(iii) and(IV) please solve it
it is urgent
(iii) ans =20
(Iv) ans =72
I need the process
please help me.​

Answer 1

3) (180-100)+3x=7x

80=4x

x=20

4) 180-(90+30)=180-(48+X)

X=72

Answer 2

(iii) x = 20 degrees

Refer to the attachment for figure and angle naming.

EXPLANATION :-

$\angle \: dac = \angle \: acb + \angle \: cba \\ \\ \\ 7x = 3x + \angle \: 1$

Reason - Exterior angle of a triangle is equal to the sum of the interior opposite angles.

Now ,

$\angle1 + \angle \: cbe = 180 \\ \\ \angle1 = 180 - 100 = 80$

Now,

Finding x :-

7x = 3x + 80

Or,

7x-3x = 80

4x = 80

x =80/4 = 20 degrees.

(IV) x = 72 degrees

EXPLANATION :-

In traingle QTR :-

$\angle2 = 180 - \angle \: rqt - \angle \: qtr \\ \\ \\ \angle2 = 180 - 48 - 90 \\ \\ \angle2 = 42 \degree$

Reason- Angle sum property of Triangle.

Now,

$in \: \triangle \: prs$

$\angle2 + \angle \: rps = \angle \: x$

Reason = Exterior angle of a triangle is equal to the sum of the interior opposite angles.

Now,

x = 30 + angle 2

x = 30 + 42

$x = 72 \degree$

Answer!