Question

Side AB of a cyclic quadrilateral ABCD is produced to a point E. if angle ADC = 120°, value of angle CBE is

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Answer 1

Answer:

∠CBE is 60°.

Step-by-step explanation:

Given :

• ABCD is a cyclic quadrilateral.
• ∠ADC is 120°.

To find :

• Measure of angle ∠CBE.

Solution :

Cyclic quadrilateral are those quadrilateral whose all vertices of quadrilateral lies of circumference of circle.

We know,

✿ Sum of opposite sides of the cyclic quadrilateral are equal to 180°.

So,

$\leadsto$ ∠CBA + ∠ADC = 180°

$\leadsto$ ∠CBA + 120° = 180°

$\leadsto$ ∠CBA = 180° - 120°

$\leadsto$ ∠CBA = 60°

Now,

We also know,

✿ Sum of all angles forms on straight line is equal to 180° we can say linear pair.

So,

$\leadsto$ ∠CBA + ∠CBE = 180°

$\leadsto$ 60° + ∠CBE = 180°

$\leadsto$ ∠CBE = 180° - 60°

$\leadsto$ ∠CBE = 120°

Thus,

Measure of ∠CBE is 120°.

Answer 2

⇝Given :-

• ABCD is a cyclic quadrilateral.
• ∠ADC = 120°

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⇝To Find :-

• Find ∠CBE .

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⇝Concept Used :-

✧ Sum of opposite sides of a cyclic quadrilateral is 180°.

✧ Sum of linear Pair is 180°.

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⇝Solution :-

❒ First finding angle CBA :

✧ Sum of opposite sides of a cyclic quadrilateral is 180°.Hence,

${:{\longmapsto{\bf{∠CBA +∠ADC = 180°}}}}$

${:{\longmapsto{\bf{∠CBA +120 = 180°}}}}$

${:{\longmapsto{\bf{∠CBA = 180° - 120}}}}$

${\large{\purple{:{\longmapsto{\underline{\overline{\boxed{\bf{∠CBA = 60°}}}}}}}}}$

❒ Now ∠CBE :

✧ Sum of linear Pair is 180°.

${:{\longmapsto{\bf{∠CBA +∠CBE = 180°}}}}$

${:{\longmapsto{\bf{60 +∠CBE = 180°}}}}$

${:{\longmapsto{\bf{∠CBE = 180° - 60}}}}$

${\large{\purple{:{\longmapsto{\underline{\overline{\boxed{\bf{∠CBE = 120°}}}}}}}}}$

❒ Hence :

${\large{\pink{\mathfrak{\underline{\purple{\underline{\red{\mathfrak{∠CBE = 120°}}}}}}}}}$

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