Question

FIND THE VALUE OF X GOVE REASONS DON'T FORGET TO GIVE REASON OR ELSE IT WILL BE REPORTED AND SPAMMERS TOO WILL BE REPORTED AND THE ANGLE NOT VISIBLE IN PICTURE IS A ​

Answer 1

$\LARGE{ \underline{\underline{ \bf{Required \: answer:}}}}$

In the figure, we can see that DC and FE are two lines parallel to each other and AB is acting as a transversal.

Then, ∠DZQ + ∠FQZ = 180°

(Interior angles on the same side of the transversal are supplementary i.e. they add upto 180°)

GiveN:

• ∠DZQ = 2x + 6°
• ∠FQZ = 3x + 54°

Then,

⇒ ∠DZQ + ∠FQZ = 180°

⇒ 2x + 6° + 3x + 54° = 180°

⇒ 5x + 60° = 180°

⇒ 5x = 120°

⇒ x = 120° / 5

⇒ x = 24°

Hence,

• The required value of x is $24°$

Explore more!!

When two parallel lines are intersected by a transversal:

• Alternate interior and Alternate exterior angles are equal.
• Corresponding angles are equal.
• Vertically opposite angles are equal.
• The interior/exterior angles on the same side of the transversal are supplementary.

Answer 2

${\underline{\underline{\sf{\large{\pink{\bigstar{\: Given : }}}}}}}$

• ∠DZQ = 2x + 6 °
• ∠FQZ = 3x + 54°

${\underline{\underline{\sf{\large{\pink{\bigstar{\: To \: find : }}}}}}}$

• Value of x :-

${\Large{\underline{\underline{\sf{\large{\red{\bigstar{\: Solution : }}}}}}}}$

Here the concept of the question is that Two parallel lines are given CD || EF and AB is the transversal in which two angles are made on the same side of interior of the transversal and we know that Angles made on the interior same side of the transversal is 180°. So, here we can write this as.

${\mathtt{\implies{ ∠DZQ + ∠FQZ = 180°}}}$

${\mathtt{\implies{2x + 6° + 3x + 54° = 180°}}}$

${\mathtt{\implies{2x + 3x + 6° + 54° = 180°}}}$

${\mathtt{\implies{5x + 60° = 180° }}}$

${\mathtt{\implies{5x = 180° - 60°}}}$

${\mathtt{\implies{5x = 120°}}}$

$\\ {\mathtt{\implies{x = \frac{120}{5} }}}$

$\large{ \orange{ \boxed{ \boxed{\mathtt{\implies{ \blue{x = 24 \degree}}}}}}}$

So, Value of x is 24°.

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For more finding all angles.

☆ First angle:-

》2x + 6 °

》2(24) + 6

》54°

So, Value of first Angle is 54°

☆Second Angle :-

》3x + 54°

》3 × 24 + 54 °

》126°

So, Value of second angle is 126°.

VERIFICATION:-

》126° + 54° = 180°

》180° = 180°

》LHS = RHS

So, our answer 24° is correct answer.