Question

please find the answer as fast as possible​

Answer 1

Solution

Given :

• CF = DE

• CD // FE

Here,

DE and FC are Transversal on the line

• CD

Given angle C = 104°

$\\ \large \sf \underline{ \underline{ \star \: \: property : }}$

Angles of different Transversals on same line are equal

$\\ \large \sf \therefore \: \angle \: c = \angle \: d = 104 \degree$

Now,

• Angle F = angle E

(as opposite lines are equal and parallel)

$\\ \large \rm \leadsto \: let \: \angle \: a = \angle \: b = x$

Solving:

$\\ \large \sf \underline{ \underline{ \star \: angle \: \: su m \: \: property: }}$

$\\ \large \tt \implies \angle \: a + \angle \: b + \angle \: c + \angle \: d = 360 \degree \\ \\ \large \tt \implies x + x + 104 \degree + 104 \degree = 360 \degree \\ \\ \large \tt \implies 2x + 208\degree = 360 \degree \\ \\ \large \tt \: \implies \: 2x = 360 \degree - 208 \degree \\ \\ \large \tt \: \implies \: 2x = 152 \degree \\ \\ \large \tt \: \implies \: x = \frac{152}{2} \\ \\ \large \tt \therefore \: \: x = 76 \degree$

So,

Angle a = angle b = 76°

__________________________________

$\\ \large \sf \underline{ \underline{ \star \: \: check : }}$

$\\ \large \sf \underline{ { \: angle \: \: su m \: \: property: }}$

angle a + angle b + angle c + angle d = 360°

$\\ \large \sf \implies \: 104 \degree + 104 \degree + 76 \degree + 76 \degree = 180\degree \\ \\ \large \sf \mapsto \: \: 360 \degree = 360 \degree \\ \\ \large \rm \: l.h.s = r.h.s$

Hence Proved