In the given figure, AB || CD, ∠ABE = 120°, ∠ECD = 100° and ∠B

1.	In the given figure, AB \|\| CD, ∠ABE = 120°, ∠ECD = 100° and ∠BEC = x°. Find the value of x
Answer» $\bf\underline{\underline{\pink{Question:-}}}$ ★In the given FIGURE, AB \|\| CD, ∠ABE = 120°, ∠ECD = 100° and ∠BEC = x°. FIND the value of x $\bf\underline{\underline{\blue{Given:-}}}$ ★In the given figure, AB \|\| CD, ∠ABE = 120°, ∠ECD = 100° $\bf\underline{\underline{\green{ToFind:-}}}$ ★The value of x $\bf\underline{\underline{\red{Construction:-}}}$ ★Through E, draw FEG \|\| AB \|\| CD. $\bf\underline{\underline{\orange{Solution:-}}}$ Now, FE \|\| AB And BE is the transversal. ∴ ∠BEF + ∠ABE = 180° ==> ∠BEF + 120° = 180° [co-interior ANGLE] ==> ∠BEF = (180° – 120°) ==> ∠BEF = 60° Again, CD \|\| EG and CE is the transversal. ∴ ∠CEG + ∠ECD = 180° [co-interior angle] ==> ∠CEG + 100° = 180° ==> ∠CEG = (180° – 100°) ==> ∠CEG = 80° Now, FEG is a straight line. ∴ ∠BEF + ∠BEC + ∠CEG = 180° ==> 60° + x° + 80° = 180° ==> x + 140° = 180° ==> x = (180° – 140°) ==> x = 40° Hence, the value of x is 40° ━─━─━─━─━──━─━─━─━─━─━─━━─━─━─━

In the given figure, AB || CD, ∠ABE = 120°, ∠ECD = 100° and ∠BEC = x°. Find the value of x

Answer»

$\bf\underline{\underline{\pink{Question:-}}}$

★In the given FIGURE, AB || CD, ∠ABE = 120°, ∠ECD = 100° and ∠BEC = x°. FIND the value of x

$\bf\underline{\underline{\blue{Given:-}}}$

★In the given figure, AB || CD, ∠ABE = 120°, ∠ECD = 100°

$\bf\underline{\underline{\green{ToFind:-}}}$

★The value of x

$\bf\underline{\underline{\red{Construction:-}}}$

★Through E, draw FEG || AB || CD.

$\bf\underline{\underline{\orange{Solution:-}}}$

Now, FE || AB And BE is the transversal.

∴ ∠BEF + ∠ABE = 180°

==> ∠BEF + 120° = 180° [co-interior ANGLE]

==> ∠BEF = (180° – 120°)

==> ∠BEF = 60°

Again, CD || EG and CE is the transversal.

∴ ∠CEG + ∠ECD = 180° [co-interior angle]

==> ∠CEG + 100° = 180°

==> ∠CEG = (180° – 100°)

==> ∠CEG = 80°

Now, FEG is a straight line.

∴ ∠BEF + ∠BEC + ∠CEG = 180°

==> 60° + x° + 80° = 180°

==> x + 140° = 180°

==> x = (180° – 140°)

==> x = 40°

Hence, the value of x is 40°

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