Exercise 19

Find the values of x and y. Then find the measures of the interior angles of the polygon.

x = 25, y = 5

The interior angles:

<ABC = 75°

<BCD = 50°

<CDA = 105°

<DAC = 130

Step-by-step explanation:

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Polygon ABCD is a cyclic quadrilateral.

For cyclic quadrilaterals, their opposite angles add up to 180°.

Meaning that;

2x + 26y = 180 ---- equation 1

and

3x + 21y = 180 ------ equation 2

These will be solved simultaneously..

Multiply ½ to both sides of equation 1

½(2x + 26y) = ½ * 180

½ * 2x + ½ * 26y = ½ * 180

x + 13y = 90

Make x the subject of formula

x = 90 - 13y

Multiply both sides of equation 2 by ⅓

⅓(3x + 21y) = ⅓ * 180

⅓ * 3x + ⅓ * 21y = ⅓ * 180

x + 7y = 60

Recall that x = 90 - 13y.

So, x + 7y = 60 becomes

90 - 13y + 7y = 60

90 - 6y = 60

Collect like terms

-6y = 60 - 90

-6y = -30

Divide both sides by -6

-6y/-6 = -30/-6

y = 5

Recall that x = 90 - 13y.

So, x = 90 - 13(5)

x = 90 - 65

x = 25

Having calculated x and y, the interior angles can then be calculated.

The interior angles of the polygon are

1. <ABC

2. <BCD

3. <CDA

4. <DAC

Recall that x = 25 and y = 5

<ABC = 3x

<ABC = 3 * 25

<ABC = 75°

<BCD = 2x

<BCD = 2 * 25

<BCD = 50°

<CDA = 21y

<CDA = 21 * 5

<CDA = 105°

<DAC = 26y

<DAC = 26 * 5

<DAC = 130

Hence,

x = 25, y = 5

The interior angles:

<ABC = 75°

<BCD = 50°

<CDA = 105°

<DAC = 130

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.