Question

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Answer 1

Answer:

This is your required answer.

Answer 2

$\mapsto\pink{\mathfrak{Given}} \begin{cases} &\sf{\angle ABC} = \bf{87^{\circ}} \\ & \sf{\angle ACE} = \bf{75^{\circ}} \\ &\sf{AB \parallel CE}\end{cases}$

$\mapsto\purple{\mathfrak{ Find}} \begin{cases} &\sf{\angle ACD} = \bf{?}\end{cases}$

$\mapsto\underline{\orange{\mathfrak{ Solution}}}$

Here, AB || CE ............[Given]

As, we know that Alternate Angles made between two parallel lines area equal.

So,

→∠BAC = ∠ACE......【Alternate Angles】

→∠BAC = 75° ..〘°•° ∠ACE = 75°〙

•°• ∠BAC = 75°

Now, we know that sum of two internal angles is equal to the opposite exterior angle.

➨ ∠ABC + ∠BAC = ∠ACD «Exterior angle»

Here, ∠ACD can be written as ∠ACE + ∠ECD

➨ ∠ABC + ∠BAC = ∠ACE + ∠ECD

Where,

• ∠ABC = 87°
• ∠BAC = 75°
• ∠ACE = 75°

★ ꜱᴜʙꜱᴛɪᴛᴜᴛɪɴɢ ᴛʜᴇꜱᴇ ᴠᴀʟᴜᴇꜱ:

➨ ∠ABC + ∠BAC = ∠ACE + ∠ECD

➨ 87° + 75° = 75° + ∠ECD

➨ 162° = 75° + ∠ECD

➨ 162° - 75° = ∠ECD

➨ 87° = ∠ECD

•°• ∠ECD = 87°

Now,

➠ ∠ACD = ∠ACE + ∠ECD

where,

• ∠ACE = 75°
• ∠ECD = 87°

✫ ꜱᴜʙꜱᴛɪᴛᴜᴛɪɴɢ ᴛʜᴇꜱᴇ ᴠᴀʟᴜᴇꜱ:

➠ ∠ACD = ∠ACE + ∠ECD

➠ ∠ACD = 75° + 87°

➠ ∠ACD = 162°

❂____________________________❂

Therefore, Value of ∠ACD is 162°