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The circle below is centred at O.
AB is a tangent to this circle.
Work out the size of angle y.
Justify your answer.
O
42°
y
A
B
Not drawn accurately

The circle below is centred at O AB is a tangent to this circle Work out the size of angle y Justify your answer O 42 y A B Not drawn accurately class=

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Answer:

y = 48°

Step-by-step explanation:

angle A = 90°

interior angles of a triangle = 180°

therefore

y = 180 - 42 - 90

y = 48°

SeraphicCirce

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❒ Given ❒

  • ➣ Mid point of a circle
  • ➣ Tangent AB
  • ➣ Angle "o" of 42⁰
  • ➣ Angle "A" of 90⁰ (cuz it is the perpendicular of traingle given in circle)

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❒ Note ❒

  • ➣here tangent AB with point O (mid point of circle) forming a traingle
  • ➣we have to find "y" in the given figure (angle B)

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❒ Concept used ❒

  • ➣The sum of interior angles of traingle is of 180⁰
  • ➣to find the missing angle ( y ) we will use this theorem
  • ➣this Concept is also know as Sum theorem

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❒ Assumption ❒

  • ➣angle B = y

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❒ Let's solve ❒

[tex] \large \pmb{➪ \: } \rm \pink{ \angle \: OAB+\angle \:ABO+\angle \:BOA = 180 \degree}[/tex]

  • ➣let's substitute value now .....

[tex] \pmb{➪ \: 90 + y +42 = 180 } \\ \pmb{➪ \:132 + y = 180 \: \: \: \: \: \: \: \: }\\ \pmb{➪ \:y = 180 - 132 \: \: \: \: \: \: \: \: }\\ \pmb{➪ \:y = 48 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]

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Hence the size of angle is

[tex] \large \boxed{✥\underline{ \boxed{ \sf{y = 48 \degree \: \pmb{\green{✓}} }}}✥}[/tex]

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Hope it helps !

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