Question

calculate the value of the x in each of the following figure
please answer with full explanation​

Answer 1

in triangle ABE

the sum of interior angle of triangle is 180°

so, <EBA + <BAE + <AEB = 180°

65° +75° + <AEB = 180°

140° +<AEB = 180°

<AEB = 180°-140°

<AEB = 40°

now <AEB = <DEC ( by vertically opposite angle )

then <DEC = 40°

In triangle DEC

the sum of interior angle is 180°

then,

<DEC + <ECD + <CDE = 180°

40° + 110° + x = 180°

150° + x = 180°

x = 180°- 150°

x= 30°

Answer 2

✫ Sum of angle of triangle = 180 degree

In triangle ABE :

$\implies \: 75 + 65 + \angle \: </em></strong><strong><em>A</em></strong><strong><em>E</em></strong><strong><em>B</em></strong><strong><em> = 180 \degree$

$\implies140 + \angle \: </em></strong><strong><em>A</em></strong><strong><em>E</em></strong><strong><em>B</em></strong><strong><em> \: = 180 - 140$

$\implies \angle \: </em></strong><strong><em>A</em></strong><strong><em>E</em></strong><strong><em>B</em></strong><strong><em> \: = 180 - 140 = 40$

By property of vertically opposite angles :

$\angle \: </em><em>A</em><em>E</em><em>B</em><em> </em><em>\: = \angle \: </em><em>D</em><em>E</em><em>C</em><em>$

As, angle AEB = 40 degree

Angle DEC is = 40 degree

Now, in triangle DEC :

$\implies \: x \degree \: + 110 \degree + 40 \degree = 180 \degree$

$\implies \: x \degree + 150 \degree = 180 \degree$

$\implies \: x \degree = 180 - 150 \degree$

$\red \implies \: x \degree \: = 130 \degree$