Question

BRAINLY STAR
MODETORS
Q)
$\large \sf \angle \: b = 105 \degree$
angle A = 25°

BD || CE

Find the value of x in the above picture.

Spam answer will be reported. ​

Answer 1

☞︎︎︎ Construction :

Since,

• Given :

DB || EC

So,

Draw CF (such as DB || EF )

➪ Finding ∠y :

Here,

105° + ∠y = 180° (allied angles)

⇒ ∠y = 180° - 105°

∠y = 75°

_____________________________________________

We know :

Angle Along straight line = 180°

$\\ \large \sf : \implies \angle \: y + \angle \: z = 180 \degree \\ \\ \large \sf : \implies 75 \degree+ \angle \: z = 180 \degree \\ \\ \large \sf : \implies \angle \: z = 180 \degree - 75 \degree\\ \\ \large \sf \therefore \: \angle \: z = 105\degree$

Now ,

In triangle AFC :

• Angle sum Property

$\\ \large \sf \rightarrow \: \angle \: z + \angle \: a + \angle \: t = 180 \degree \\ \\ \large \sf : \implies\: 105 \degree + 25 \degree + \angle \: t = 180 \degree \\ \\ \large \sf : \implies\: 130 \degree + \angle \: t = 180 \degree \\ \\ \large \sf : \implies\: \angle \: t = 180 \degree - 130 \degree \\ \\ \large \sf \therefore \: \underline{ \underline{ \angle \: t = 50 \degree}}$

_____________________________________________

Angels along straight line = 180°

$\large \sf \implies \angle \: t + \angle \: x = 180 \degree \\ \\ \large \sf \implies 50 \degree + \angle \: x = 180 \degree \\ \\\large \sf \implies \angle \: x = 180 \degree - 50 \degree\\ \\ \large{ \underline{\boxed{ \sf \angle \: x = 130 \degree}}}$