For this problem, we are given a parallelogram with a diagonal drawn, inside it there are markings for a few angles. We need to determine the unknown angles.

Opposite sides of a parallelogram are parallel, this means we can treat the diagonal as a transversal line that crosses two parallel lines. Since this is the case, the angles 33º and xº are alternate interior angles and have the same length:

$x=33º$

The opposite angles in a parallelogram are congruent, therefore:

$z=109º$

The sum of internal angles is 360º, therefore we have:

$\begin{gathered} 2\cdot109+2\cdot(x+y)=360\\ \\ 218+66+2y=360\\ \\ 284+2y=360\\ \\ 2y=360-284\\ \\ 2y=76\\ \\ y=38 \end{gathered}$

The value of x is 33º, the value of y is 38º and the value of z is 109º.

4 0

1 year ago

If nis the larger of two consecutive numbers, write an expression for the other number.

allochka39001 [22]

Answer:

n-1

Step-by-step explanation:

Consecutive means that they have a difference of one, so the expression will be n-1.

8 0

3 years ago

Read 2 more answers

3/4+5/36+7/144+.......+17/5184+19/8100<br><br>(a)0.95 (b)1 (c) 0.99 (d)0.98

abruzzese [7]

Answer:

B) 1

Step-by-step explanation:

All I did was simplify the equation

1509/1600

(Decimal: 0.943125)

HOPE THIS HELPS!!!! :)

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4 0

3 years ago

Choose the equation of a circle with radius 6 and center (2, -3).

Rufina [12.5K]

Answer: $(x-2)^2 + (y+3)^2 = 36\\\\$

Work Shown:

$(x-h)^2 + (y-k)^2 = r^2\\\\(x-2)^2 + (y-(-3))^2 = 6^2\\\\(x-2)^2 + (y+3)^2 = 36\\\\$

Note that (h,k) = (2,-3) is the center and r = 6 is the radius. The last line is not expanded out using the FOIL rule because its common practice to leave it in $(x-h)^2 + (y-k)^2 = r^2\\\\$ form. This form allows the reader to quickly determine the center and radius (rather than have to do a lot of algebraic steps before hand).

3 0

2 years ago