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Morgarella [4.7K]
3 years ago
9

∠ABD is formed by a tangent and a secant intersecting outside of a circle. If minor arc AC = 72° and minor arc CD = 132°, what i

s the measure of ∠ABD?

Mathematics
1 answer:
Kruka [31]3 years ago
8 0

Answer:

measure of ∠ABD = 42°

Step-by-step explanation:

Angle Formed by Tangent and Secant = (1/2)*(difference of Intercepted Arcs)

In this case the intercepted arcs are: minor arc AC and minor arc AD. Let´s first find minor arc AD, we know that:

minor arc AC + minor arc CD + minor arc AD = 360°

Then,

minor arc AD = 360° - minor arc AC - minor arc CD

minor arc AD = 360° - 72° - 132°

minor arc AD = 156°

Replacing in the aforementioned formula:

Angle Formed by Tangent and Secant = (1/2)*(difference of Intercepted Arcs)

∠ABD = (1/2)*(minor arc AD - minor arc AC)

∠ABD = (1/2)*(156° - 72°)

∠ABD = 42°

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Answer/Step-by-step explanation:

A linear pair is formed when two straight lines intersect to form two angles that are adjacent to each other and are on a straight line. The sum of both adjacent angles equals 180°.

From the diagram given, examples of linear pair are:

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6 0
2 years ago
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Answer:

x = \frac{3}{4}

Step-by-step explanation:

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2 years ago
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8 0
3 years ago
Eighth grade
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Answer:

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Now, simplifying the terms with 'b'.

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2 years ago
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8 0
3 years ago
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