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Veronika [31]
3 years ago
6

In the figure below AB is a diameter of circle P. What is the arc measure of minor arc AC in degrees? ​

Mathematics
1 answer:
arlik [135]3 years ago
3 0

Answer:

P = 139

Step-by-step explanation:

See attachment for complete question

Required

Determine measure of Arc length AC

The interpretation of this question is to find P

If AB is the diameter, then

P + 41 = 180

P + 41 - 41= 180 - 41

P = 139

<em>Hence, the measure is 139 degrees</em>

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Answer:

a. i. x + y = 180  (1) and  x - 4y = 5   (2)

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Step-by-step explanation:

a. The measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles. Write and solve a system of equations to find the measures of all the angles.

i. Write a system of equations to find the measures of all the angles.

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Since we have two obtuse angles at the top of the isosceles trapezoid and two acute angles at the bottom of the isosceles trapezoid, and also, since the sum of angles in a quadrilateral is 360, we have

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Its is also given that the measures of the obtuse angles in the isosceles trapezoid are five more than four times the measures of the acute angles.

So, x = 4y + 5   (2)

x - 4y = 5   (2)

So, our system of equations are

x + y = 180  (1) and  x - 4y = 5   (2)

ii. Solve a system of equations to find the measures of all the angles.

Since

x + y = 180  (1) and  x - 4y = 5   (2)

Subtracting (2) from (1), we have

x + y = 180  (1)

-

x - 4y = 5   (2)

5y = 175

dividing both sides by 5, we have

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So, the two acute angles are 35° each and the two obtuse angles are 145° each.

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