Question

please find this lines and angles ​

Answer 1

$\huge\bigstar\underline\color{aqua}explanation : -$

☆To find:-

● The value of angle ECP

☆Given:-

● AFE= 30 ° and AEF is a right angled triangle and AB ||CD

☆Note :-

• Sum of all interior angles of triangle is 180 °

• Vertically opposite angles are equal

• Sum of interior consecutive angles is 180°

☆Solution:-

● We know, In triangle AEF

--> AFE +FAE +AEF = 180°

--> 30 ° +90° + AEF =180°

--> 120 ° +AEF =180°

--> AEF = (180-120)°

--> AEF =60°

● Given,AB||CD and EC is the transversal .

● Now ,angles AEF = BEC ( vertically opposite angles)

● Therefore, Angle BEC = 60°.

●Now,angleBEC +ECD=180°( Consecutive interior angles)

--> 60° + ECD = 180°

--> ECD = (180 - 60)°

--> ECD = 120 °

☆Hence: -

● Angle ECD = 120°

$\bigstar\underline\color{violet}is \: the \: required \: answer \:$

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☆ Some lines and angles theorem and axoms :-

• Sum of the angles of a linear pair is180

• If two lines intersect then the vertically opposite angles are equal.

• If a transversal cuts two parallel lines then each pair of corresponding angles are equal.

• If a transversal cuts two parallel lines then alternate angles of each pair are equal.

• If a transversal cuts two parallel lines then each pair of consecutive angles are supplementary .

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hope it helps.... :)