Question

Please answer me I have exam on Monday
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Answer 1

Step-by-step explanation:

angle CEF + angle ECD

= 30° + 150°

= 180°

Since, the sum is 180°, therefore these angles are co interior.

Therefore, EF || CD (eq 1)

angle BCD = angle BCE + angle ECD

angle BCD = 36° + 30°

angle BCD = 66°

Since,

angle ABC = angle BCD

Therefore, these angles are alternate interior angles.

Therefore, AB || CD (eq 2)

From equation 1 and 2,

AB || EF

Hence proved

Hope it helps!

Mark me brainliest!

Answer 2

$\huge\underline\mathfrak\red{Answer:}$

$\textbf{\underline{\underline{To\:Show\:AB\:Is\: Parallel\:To\:EF}}}$

Before Showing this We have to prove that AB is parallel to CD and CD is parallel to EF

$\textbf{\underline{\underline{1. To\:Show\:AB\:Is\: Parallel\:To\:CD}}}$

Given,

$\angle \sf ABC = {66} \degree$

$\angle \sf BCD = 36 \degree + {30} \degree = {66} \degree$

$\angle\:ABC = \angle\:BCD$ (Alternate Angles)

So, AB || CD => eq...(i)

$\textbf{\underline{\underline{1. To\:Show\:CD\:Is\: Parallel\:To\:EF}}}$

$\angle \sf \: FEC + \angle \sf \: \: ECD = 180 \degree$

$150 \degree + 30 \degree = 180 \degree$

(Sum of Corresponding is 180°)

So, CD || EF => eq...(ii)

From, eq...(i) and eq...(ii)

AB || EF

$\huge{\boxed{\tt{Proved}}}$