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3 years ago

In the circle, O is the centre and AB is a diameter.

Mathematics

1 answer:

Burka [1]3 years ago

7 0

Answer:

Step-by-step explanation:

Answer:

a). m∠a = 62°

b). m∠b = 118°

Step-by-step explanation:

a). Since, an angle inscribed in a semicircle is a right angle,

m∠ACB = 90°

By triangle sum theorem in ΔABC,

m∠CAB + m∠ACB + m∠ABC = 180°

28° + 90° + m∠ABC = 180°

118° + m∠ABC = 180°

m∠ABC = 180°- 118°

a = 62°

b). Since, quadrilateral ABCD is a cyclic quadrilateral,

m∠ADC + m∠ABC = 180°

b + a = 180°

b + 62° = 180°

b = 180° - 62°

b = 118°

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a reflection over the x-axis and then a 90 degree clockwise rotation about the origin

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Lets suppose triangle JKL has the vertices on the points as follows:

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30 years ago zoe was 2/3 as old as luke, 18 years ago zoe was 5/6 as old as luke how old are they now

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Based on the mathematical statements, Zoe is 56 years old and Luke is 66 years old, now

<h3>How to determine how old they are now?</h3>

From the question, we have the following statements that can be used in our computation:

<u>30 years ago</u>

Zoe was 2/3 as old as Luke

<u>18 years ago</u>

Zoe was 5/6 as old as Luke

Let their present ages be represented as

Zoe = x

Luke = y

So, we have the following representations

<u>30 years ago</u>

Zoe was 2/3 as old as Luke

x - 36 = 2/3(y - 36)

<u>18 years ago</u>

Zoe was 5/6 as old as Luke

x - 18 = 5/6(y - 18)

So, we have the following system of equations

x - 36 = 2/3(y - 36)

x - 18 = 5/6(y - 18)

Make x the subject in x - 18 = 5/6(y - 18)

x = 5/6(y - 18) + 16

Substitute x = 5/6(y - 18) + 16 in x - 36 = 2/3(y - 36)

5/6(y - 18) + 16 - 36 = 2/3(y - 36)

Open the brackets

5/6y - 15 + 16 - 36 = 2/3y - 24

Evaluate the like terms

5/6y - 35 = 2/3y - 24

Multiply through by 6

5y - 210 = 4y - 144

Evaluate the like terms

y = 66

Substitute y = 66 in x = 5/6(y - 18) + 16

x = 5/6(66 - 18) + 16

Evaluate

x = 56

Recall that

Zoe = x

Luke = y

So, we have

Zoe = x = 56

Luke = y = 66

Hence, they are 56 and 66 years, now