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2 years ago

Find the values of a and b. a The diagram is not drawn to scale. a = U b = U

Mathematics

1 answer:

nata0808 [166]2 years ago

7 0

Answer:

a = 36°

b = 144°

Step-by-step explanation:

<h3><u>Method 1</u></h3>

Number of sides = n = 10

Sum of interior angles = (n - 2) × 180°

= (10 - 2) × 180°

= 8 × 180°

= 1440°

Interior angle = b = sum of interior angles ÷ number of sides

b = 1440 ÷ 10

b = 144°

a + b = 180° (Sum of angles in the straight line)

a + 144° = 180°

a + 144° - 144° = 180° - 144°

a = 36°

<h3><u>Method 2</u></h3>

Number of sides = 10

Exterior angle = a = 360° ÷ Number of sides

a = 360° ÷ 10

a = 36°

a + b = 180° (Sum of angles in the straight line)

36° + b = 180°

36° + b - 36° = 180° - 36°

b = 144°

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Serjik [45]

I would say either a or b

3 0

3 years ago

CD is perpendicular to AB and passes through point C5, 12).

Aleksandr-060686 [28]

Answer:

x intercept of CD = 17

Step-by-step explanation:

We are given a line AB with its end coordinates. and Another line segment CD which is perpendicular to AB. We have the coordinates of C , and we are asked to find the x intercept of line CD.

For that we need to find the equation of CD

we have coordinates of C , and hence if we have slope of CD we can find equation of CD

Slope of CD can be determine with the help of slope of AB as CD⊥ AB

So, the slope of CD $mCD = -\frac{1}{mAB}$

Hence we start from determining slope of AB

slope is given as

$m= \frac{y_2-y_1}{x_2-x_1}$

$m= \frac{14-(-3)}{7-(-10)}=\frac{17}{17}=1$

Hence $mAB=1$

There fore $mCD=-1$

(∵ Product of Slopes of two perpendicular lines is always -1)

Now we find the equation of CD with the help of slope -1 and coordinates of C(5,12)

$m=\frac{y-y_1}{x-x_1}$

$-1=\frac{y-12}{x-5}$

$-x+5=y-12$

$y=-x+17$

Hence we have our equation , now in order to find the x intercept we keep y = 0 in it and solve for x

$0=-x+17$

$x=17$

Hence the x intercept is 17

8 0

3 years ago

Which equation is a point slope form equation for line AB ?

zepelin [54]

(-2,3)(4,-1)
slope = (3 + 1)/(-2 - 4) = 4/-6 = -2/3

equation
y + 1 = -2/3(x - 4)

7 0

4 years ago

Present a picture of an object (TV, Ipad Screen, Book Cover) that contains a right angle (it could be something in nature or tha

myrzilka [38]

The measure of hypotenuse using the ruler is 25.5 cm and using the formula is 23.43 cm, they are not same, and formula can be used to in the real life problems as well.

<h3>What is a right-angle triangle?</h3>

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

The question is incomplete:

The complete question is:

Present a picture of an object (TV, Ipad Screen, Book Cover) that contains a right angle (it could be something in nature or that is man-made). Use a ruler or measuring tape to measure the two sides that make the right angle and measure the distance from the end of one side to the end of the other side (hypotenuse). Draw a diagram of the object including the measurements. Use your leg measurements on your diagram to calculate a theoretical hypotenuse. (Show all steps).

Does the hypotenuse that measured with a ruler/measuring tape equal the hypotenuse you calculated?
Why do you think they are or are not exactly the same?
What did you learn from developing this presentation?

We are assuming the length of one side x:

x = 18 cm

Length of other side y:

y = 15 cm

And length of the hypotenuse z:

z = 23.5 cm

From the Pythagoras theorem:

z² = x² + y²

z² = 18² + 15²

z² = 549

z = √54 = 23.43 cm

The measure of hypotenuse is:

Using ruler: x = 25.5 cm

Using formula: x = 23.43 cm

They are not equal due to the reading in the ruler.

The formula can be used to in the real life problems as well.

Thus, the measure of hypotenuse using the ruler is 25.5 cm and using the formula is 23.43 cm, they are not same, and formula can be used to in the real life problems as well.

Learn more about the right angle triangle here:

brainly.com/question/3770177

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