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Emiann222
09.10.2019 •
Mathematics
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in the diagram of circle o, what is the measure of angle abc?
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Ответ:
∠ABC=30°
Given: A circle with center O. Two tangents AB and BC are making angle ABC with arc at circle 150°.
To find : ∠ABC
Solution: We know that the angle formed by the intersection of two tangents outside the circle equals to the half of difference of the intercepted arcs.[major arc and minor arc]
From the figure ,Minor arc = 150°
Major arc = 360 - 150 = 210°
Therefore,∠ABC =![\frac{210^{\circ}-150^{\circ}}{2}=\frac{60^{\circ}}{2}=30^{\circ}](/tpl/images/0305/0025/d6c80.png)
Thus ∠ABC=30°.
Ответ:
Measure of Angle ABC is 30°
Step-by-step explanation:
Given: Circle with centre O and Tangents AB & BC.
To find: m∠ABC.
Construction: Join Radius OA & OC. (New Figure is attached)
Given Value of Arc AC is 150°. It means 150° is measure of angle by which that arc is suspended.
⇒ m∠AOC = 150°.
m∠BAO = m∠BCO = 90° ( because Tangent and Radius are perpendicular to each other at point of contact i.e., A & B )
ABCO is a Quadrilateral.
∴ using Angle Sum Property of Quadrilateral which states that sum of all interior angles of quadrilateral is 360° , we get
∠BAO + ∠BCO + ∠ABC + ∠AOC = 360
⇒ 90 + 90 + ∠ABC + 150 = 360
⇒ ∠ABC + 330 = 360
⇒ ∠ABC = 30°
Measure of Angle ABC is 30° .
Ответ:
theres no question
Step-by-step explanation: