Question

In the given figure, AB || CD || EF. If ∠BCE = 35°

and ∠CEF = 135°, then find the measure of

∠ABC.


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Answer 1

$\huge\fcolorbox{violet}{pink}{Hello}$

∠ᴇᴄᴅ = 180°-135°= 45°{ᴄᴏ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ}

∠ʙᴄᴅ= 35°+45°= 80°

∠ᴀʙᴄ=80° (ᴀʟᴛᴇʀɴᴀᴛᴇ ɪɴᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)

Answer 2

Given

• ∠BCE = 35°
• ∠CEF = 135°

To Find

The value of ∠ABC.

Solution

We know,

→ ∠CEF + ∠ECD = 180°   [Co-interior angles]

• CD || EF

→ 135° + ∠ECD = 180°

→ ∠ECD = 180° - 135°

→ ∠ECD = 45°

$\rule{150}2$

Again,

∠ABC = ∠BCD  [Alternate interior angles]

• AB || CD

→ ∠ABC = ∠ECD + ∠BCE

→ ∠ABC = 45° + 35°

→ ∠ABC = 80°     ...[Answer]