Question

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Answer 1

Question :-

Find a, b and c.

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Solution :-

➲ Given Information :-

• ∠c
• ∠b
• ∠a
• 48°

➲ To Find :-

• ∠c
• ∠b
• ∠a

➲ Concept :-

• Parallel Lines and Transversal

➲ Formulae Used :-

• Sum of angles formed on a Straight Line = 180°
• Vertically Opposite Angles
• Corresponding Angles

➲ Diagram :-

• Attached above, for reference.

➲ Explanation :-

• ∠c equals 48°

(reason is Vertically Opposite Angles)

• ∠c equals ∠a

(reason is Corresponding Angles)

• ∠b equals 180° - ∠a

(reason is Angles formed on a Straight Line = 180°)

➲ Calculations :-

:⇒ ∠c equals 48° (reason is Vertically Opposite Angles)

$\bf{ : \implies \: \angle c = \blue{ 48 \degree} }\: \sf \red{(vertically \: opposite \: angles)}$

:⇒ ∠c equals ∠a (reason is Corresponding Angles)

$\bf{ : \implies \: \angle a = \angle c = \blue{48 \degree}} \: \sf \red{(corresponding \: angles)}$

:⇒ ∠b equals 180° - ∠a (reason is Angles formed on a Straight Line = 180°)

$\bf{ : \implies \: \angle b = 180 \degree - 48 \degree = \blue{132 \degree}} \: \sf \red{(angles \: on \: a \: straight \: line = 180 \degree)}$

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Final Answers :-

1. ∠a = 48°
2. ∠b = 132°
3. ∠c = 48°

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Note :-

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