Question

চিত্রে, BA ও CE রেখাদ্বয় পরস্পর সমান্তরাল।
(ক) ZBAC ও ZACE এর মধ্যে সম্পর্ক লিখ।
(খ) দেখাও যে, ZBAC +ZABC =ZAcD।
(গ) প্রমাণ কর যে,ZABC +ZBCE = দুই সমকোণ।
।​

Answer 1

Given:

BA and CE are parallel lines

To find:

a) Write the relation between angle BAC and angle ACE

b) Prove that ∠BAC + ∠ABC = ∠ACD

c) Prove that ∠ABC + ∠BCE = 2 right angles

Solution:

Case (a): Finding the relation between ∠BAC and ∠ACE:

Since BA and CE are given as parallel lines and the line AC is a transversal line that crosses through the two parallel lines.

∴ ∠BAC = ∠ACE ...... [alternate angles]

Thus, the relation between angle BAC and angle ACE  are → $\boxed{\bold{They \:are\: alternate \:angles\: and \:are\: congruent\: to\: each \:other.}}$

Case (b): Proving ∠BAC + ∠ABC = ∠ACD :

In Δ ABC, we have

∠BAC + ∠ABC + ∠ACB = 180° ..... [Angle sum property of a triangle] .... (i)

Also, ∠ACB + ∠ACD = 180° ..... [Linear pair] ..... (ii)

Comparing (i) & (ii), we get

∠BAC + ∠ABC + ∠ACB = ∠ACB + ∠ACD

⇒ ∠BAC + ∠ABC + ∠ACB - ∠ACB = ∠ACD

⇒ ∠BAC + ∠ABC = ∠ACD

Hence proved, $\boxed{\bold{\angle BAC + \angle ABC = \angle ACD}}$.

Case (c): Proving ∠ABC +∠BCE = 2 right angles :

We know,

∠BAC + ∠ABC + ∠ACB = 180° ..... [Angle sum property of a triangle]

substituting from case (a) ∠BAC = ∠ACE, we get

⇒ ∠ACE + ∠ABC + ∠ACB = 180°

from the figure attached below we get → ∠ACE + ∠ACB = ∠BCE

⇒ ∠ABC + ∠BCE = 180°

we know that a right angle is the angle which measures 90°

∴ 90° + 90° = 180° represents 2 right angles

⇒ ∠ABC + ∠BCE = 180° = 2 right angles

Hence proved, $\boxed{\bold{\angle ABC + \angle BCE = 2 \:right\: angles}}$.

---------------------------------------------------------------------------------------

Also View:

Ray AB∥ ray CE, ∠APC = 100°, ∠BAD= 56°, Find m∠PCD = ?

https://brainly.in/question/22283785

In the adjoining figure, it is given that CE Parallel line BA angle BAC = 80°and angle ECD=35° find Angle ACE, angle ACB, angle ABC?

https://brainly.in/question/7696889

In the given figure, AB parallel to CD and a transversal EF cuts them at G and H respectively. If GL and HM are the bisectors of the alternate angles angle AGH and angle GHA respectively, prove that GL parallel to HM

https://brainly.in/question/2698440