oakst1 oakst1
  • 08-03-2019
  • Mathematics
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Why is this divided by 2? Measure A = 31°. Click picture

Why is this divided by 2 Measure A 31 Click picture class=

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kudzordzifrancis
kudzordzifrancis kudzordzifrancis
  • 17-03-2019

ANSWER

[tex]m\angle A = 31 \degree[/tex]

EXPLANATION

This is a Circle Theorem .

The angle created by an arc at the center of a circle is twice the angle created at the circumference by the same arc.

This implies that

[tex]m\angle B=2m\angle A[/tex]

In other words;

[tex] \frac{m\angle \:B }{2} =m\angle A[/tex]

[tex]m\angle B + 298 = 360[/tex]

[tex]m\angle B = 360 - 298 = 62 \degree[/tex]

[tex]\frac{62 }{2} =m\angle A[/tex]

[tex]m\angle A = 32 \degree[/tex]

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