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:

The question has no attachment. See attachment for complete question.

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 answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.