Question

Please explain this question ​

Answer 1

Answer:

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Answer 2

$\blue\bigstar$ Answer:

• $\rm\boxed{ x\: = \:{130}^{\circ}\:}$

$\blue\bigstar$ Given:

• l || m
• $\angle$A = ${100}^{\circ}$
• $\angle$B = ${30}^{\circ}$

$\blue\bigstar$To find:

• The value of x.

$\blue\bigstar$ Construction:

• Extend CE to D.

$\blue\bigstar$ Solution:

$\because$l || m and AD is the transversal,

$\therefore$ $\rm \boxed{\angle 1 \: = \: \angle FAD\: = \:{100}^{\circ}\:}$

( Corresponding Angles )

$\rm \boxed{\therefore \angle 1 \: = \: {100}^{\circ} \:}$

Now in $\triangle$BDE,

$\because$$\angle$1 + $\angle$EBD + $\angle$BED = ${180}^{\circ}$

( Angle Sum Property Of A Triangle)

$\implies$ 100° + 30° + $\angle$BED = 180°

( By substituting their values)

$\implies$ 130° + $\angle$BED = 180°

$\implies$ $\angle$BED = 180° - 130°

$\implies$ $\rm \boxed {\angle BED\: = \:{50}^{\circ}\: }$

$\rm \boxed {\therefore \angle BED\: = \:{50}^{\circ}\:}$

Now,

$\because$ $\angle$BED + x = 180°

( Linear Pair )

$\implies$ 50° + x = 180°

(By substituting the value of $\angle$BED)

$\implies$x = 180° - 50°

$\implies$ $\rm\boxed{x \: = \: {130}^{\circ} \:}$

$\rm\boxed{\therefore x\: = \: {130}^{\circ}\: }$

$\blue\bigstar$ Concepts Used:

• Corresponding Angles
• Angle Sum Property Of A Triangle
• Linear Pair

$\green\bigstar$Extra - Information:

• The sum of the co - interior angles is 180°. (Angles on the same side of transversal)
• Alternate Interior angles and Alternate Exterior angles are equal.
• Vertically Opposite angles are equal.
• When the sum of two adjacent angles is 180°, then they are called a linear pair of angles.