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lubasha [3.4K]
3 years ago
5

I need with this and please show workkk

Mathematics
1 answer:
trasher [3.6K]3 years ago
6 0

Answer:

1. ∠1 = 120°

2. ∠2 = 60°

3. ∠3 = 60°

4. ∠4 = 60°

5. ∠5 = 75°

6. ∠6 = 45°

Step-by-step explanation:

From the diagram, we have;

1. ∠1 and the 120° angle are corresponding angles

Corresponding angles are equal, therefore;

∠1 = 120°

2. ∠2 and the 120° angle are angles on a straight line, therefore they are supplementary angles such that we have;

∠2 + 120° = 180°

∠2 = 180° - 120° = 60°

∠2 = 60°

3. Angle ∠3 and ∠2 are vertically opposite angles

Vertically opposite angles are equal, therefore, we get;

∠3 = ∠2 = 60°

∠3 = 60°

4. Angle ∠1 and angle ∠4 an=re supplementary angles, therefore, we get;

∠1 + ∠4 = 180°

∠4 = 180° - ∠1

We have, ∠1 = 120°

∴ ∠4 = 180° - 120° = 60°

∠4 = 60°

5. let the 'x' and 'y' represent the two angles opposite angles to ∠5 and ∠6

Given that the two angles opposite angles to ∠5 and ∠6 are equal, we have;

x = y

The two angles opposite angles to ∠5 and ∠6 and the given right angle are same side interior angles and are therefore supplementary angles

∴ x + y + 90° = 180°

From x = y, we get;

y + y + 90° = 180°

2·y = 180° - 90° = 90°

y = 90°/2 = 45°

y = 45°

Therefore, we have;

∠4 + ∠5 + y = 180° (Angle sum property of a triangle)

∴ ∠5 = 180 - ∠4 - y

∠5 = 180° - 60° - 45° = 75°

∠5 = 75°

6. ∠6 and y are alternate angles, therefore;

∠6 = y = 45°

∠6 = 45°.

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<h3><u>Mean</u></h3>

<u />

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\begin{aligned}\displaystyle \textsf{Standard Deviation (Nilo)} & =\sqrt{\dfrac{(5^2+6^2+14^2+15^2)-\dfrac{(5+6+14+15)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{482-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{82}{3}}\\\\& = 5.23\end{aligned}

\begin{aligned}\displaystyle \textsf{Standard Deviation (Lisa)} & =\sqrt{\dfrac{(8^2+9^2+11^2+12^2)-\dfrac{(8+9+11+12)^2}{4}}{4-1}}\\\\& = \sqrt{\dfrac{410-\dfrac{40^2}{4}}{3}}\\\\& = \sqrt{\dfrac{10}{3}}\\\\& = 1.83\end{aligned}

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Nilo has a mean score of 10 and a standard deviation of 5.23.

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The <u>mean</u> scores are the <u>same</u>.

Nilo's standard deviation is higher than Lisa's.  Therefore, Nilo's test scores are more <u>spread out</u> that Lisa's, which means Lisa's test scores are more <u>consistent</u>.

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