Question

please explain this and tell the answer this question​

Answer 1

Answer:

30°

Interior Alternate Angle

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Answer 2

Answer:

x = 50

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Step-by-step explanation:

Given:

AB is parallel to CD

∠ECD = 100°

∠CEA = x°

∠EAB = 50°

• Let us extend the line AC (like in fig 1 in the image attached) so that it touches the line AB. this forms EF.

• Since CD and AB are parallel to and EF cuts through AB (fig 1), EF is a transversal.
• we can say that ∠ECD = ∠CFB = 100° since ∠ECD and ∠CFB are corresponding and corresponding angles in a transversal (fig 2) are always equal.
• now since we know that ∠CFB = 100, Let us use the Linear pair theorem to find ∠EFA

According to Linear pair theorem, if a ray passes through a line, the sum of the adjacent angles formed is 180, so we can say that, (fig 3.)

∠AFC + ∠CFB = 180, since AB is a straight line and CF is the ray that passes through it.

now we substitute the values and finally, we get ∠AFC as 80°

we now know the values of ∠EAF and ∠EFA (50° and 80°)

Let us take the triangle AEF. fig 4

• since we know ∠A and ∠F we can find out ∠E (i.e, $x$) by using angle sum property.
• angle sum property of triangle states that the sum of all the interior angles of a triangle should be equal to 180.

so, ∠EAF + ∠AEF + ∠EFA = 180

if you have any questions, please ask me in the comments!!