Question

l parallel to M find the value of x in the given​

Answer 1

Answer :-

• Value of x = 110°

Given :-

• L || M
• ∠ACP = 110°

To Find :-

• Value of x = ?

Explanation :-

In order to find the value of 'x', first we need to understand 2 theorems.

• Alternate angles theorem - The alternate interior angles theorem states that, the alternate interior angles are congruent when the transversal intersects two parallel lines.

• Vertically opposite angles- In a pair of intersecting lines the vertically opposite angles are equal

︻︻︻︻︻︻︻︻︻︻︻︻︻︻︻︻

$\bigstar \rm \: As \; L \parallel M, \\ \\ \\ \rm \longrightarrow \angle ACP = \angle CDM \qquad \bold{[Alternate \: Angles]} \\ \\ \rm \longrightarrow \angle CDM = 110^\circ$

︼︼︼︼︼︼︼︼︼︼︼︼︼︼︼︼

Now,

︻︻︻︻︻︻︻︻︻︻︻︻︻︻︻︻

$\bigstar \rm \: As \; QM \parallel AB, \\ \\ \\ \rm \longrightarrow \angle QDB = \angle CDM \qquad \bold{[V.O.A]} \\ \\ \bf \longrightarrow x = \red{110^\circ}$

︼︼︼︼︼︼︼︼︼︼︼︼︼︼︼︼

Hence, the value of 'x' is 110°