Question

if line AB and CD are parallel . find the value of x . solve it please . photo given​

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION\: \: } \mid}}}}}$

$\sf{ In \: \: the \: \: diagram, \red{AB \parallel CD} \: \: and \: \: \red{LM } \: \: is \: \:} \\ \sf{ the \: \: intersector.} \\ \\ \: \: \: \: \: \: \: \: \sf{ \red{LM} \: \: intersect \: \: \red{AB} \: \: line \: \: at \: \: the \: \: point \: \:} \\ \sf{ \red{P }\: \: and \: \: \red{CD }\: \: line \: \: at \: \: the \: \: point \: \: \red{Q.}}$

$\underline{ \mathfrak {\: \: Given, \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{ \red{\angle CPM = 106 \degree}} \\ \: \: \: \: \: \: \: \: \: \tt{ \red{\angle AQM = 3x + 2x}} \\ \\ \underline{ \mathfrak{ \: </p><p> \: To \: \: find : \to \: }} \\ \\ \: \: \: \: \: \: \huge{ \tt{The \: \: value \: \: of \: \: \red{ x } = \: ? }}$

$\underline{ \mathfrak{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \text{ \pink{When a intersector intersects two parallel} } \\ \text{ \pink{lines, their corresponding angles are equal.}}$

$\underline{ \text{ \: In \: \: the \: \: figure, \: }} \\ \\ \: \: \: \: \: \: \: \: \: \tt{ \red{AB } \parallel \red{CD} \: \: and \: \: \red{ LM } \: \: is \: \: the \: \: intersector \: \: } \\ \tt{which \: \: intersect \: \: \red{AB} \: \: and \: \: \red{CD} \: \: parallel \: \: } \\ \tt{ lines \: \: at \: \: point \: \: \red{P} \: \: and \: \: \red{Q } \: \: respectively.}$

$\mathfrak{So,} \\ \\ \tt{\angle CPM \: \: and \: \: \angle AQM \: \: are \: \: corresponding \: \: angles. } \\ \\ \: \: \: \: \: \tt{\therefore \angle CPM = \angle AQM} \\ \\ \tt{ \implies \: 106\degree = 3x + 2x} \\ \\ \tt{ \implies \: 106\degree = 5x} \\ \\ \tt{ \implies \:x = \frac{106 \degree}{5} } \\ \\ \: \: \: \: \: \tt{ \therefore \: \: x = 21.2 \degree \: }$

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathcal{ \pink{ \: \: SOLUTION\: \: } \mid}}}}}$

$\bf{ In \: \: the \: \: diagram, \pink{AB \parallel CD} \: \: and \: \: \pink{LM } \: \: is \: \:} \\ \bf{ the \: \: intersector.} \\ \\ \: \: \: \: \: \: \: \: \bf{ \pink{LM} \: \: intersect \: \: \pink{AB} \: \: line \: \: at \: \: the \: \: point \: \:} \\ \bf{ \red{P }\: \: and \: \: \pink{CD }\: \: line \: \: at \: \: the \: \: point \: \: \pink{Q.}}$

$\underline{ \bf{\: \: Given, \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \sf{ \pink{\angle CPM = 106 \degree}} \\ \: \: \: \: \: \: \: \: \: \sf{ \pink{\angle AQM = 3x + 2x}} \\ \\ \underline{ \bf{ \: \: To \: \: find : \mapsto \: }} \\ \\ \: \: \: \: \: \: \huge{ \sf{The \: \: value \: \: of \: \: \pink{ x } = \: ? }}$

$\underline{ \bf{ \: \: We \: \: know \: \: that, \: \: }} \\ \\ \text{\red{When a intersector intersects two parallel} } \\ \text{ \red{lines, their corresponding angles are equal.}}$

$\underline{ \sf{ \: In \: \: the \: \: figure, \: }} \\ \\ \: \: \: \: \: \: \: \: \: \sf{ \blue{AB } \parallel \blue{CD} \: \: and \: \: \blue{ LM } \: \: is \: \: the \: \: intersector \: \: } \\ \sf{which \: \: intersect \: \: \blue{AB} \: \: and \: \: \blue{CD} \: \: parallel \: \: } \\ \sf{ lines \: \: at \: \: point \: \: \blue{P} \: \: and \: \: \blue{Q } \: \: respectively.}$

$\bf{So,} \\ \\ \sf{\angle CPM \: \: and \: \: \angle AQM \: \: are \: \: corresponding \: \: angles. } \\ \\ \: \: \: \: \: \sf{\therefore \angle CPM = \angle AQM} \\ \\ \sf{ \rightarrow \: 106\degree = 3x + 2x} \\ \\ \sf{ \rightarrow \: 106\degree = 5x} \\ \\ \sf{ \rightarrow \:x = \frac{106 \degree}{5} } \\ \\ \: \: \: \: \: \sf{ \therefore \: \: \red{x = 21.2 \degree} \: }$