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:
The opposite angles in a parallelogram are congruent, therefore:
The sum of internal angles is 360º, therefore we have:
The value of x is 33º, the value of y is 38º and the value of z is 109º.
For number 1, theat is not a right triangle as a squared plus b squared does not equal c squared
1) All angles of a rectangle are right angles, so the measure of angle CBA is 90 degrees.
2) Since all angles of a rectangle are right angles, angle BAD measures 90 degrees. Subtracting the 25 degrees of angle BAW from this, we get that angle CAD has a measure of 65 degrees.
3) Opposite sides of a rectangle are parallel, so by the alternate interior angles theorem, the measure of angle ACD is 25 degrees.
4) Because diagonals of a rectangle are congruent and bisect each other, this means BW=WA. So, since angles opposite equal sides in a triangle (in this case triangle ABW) are equal, the measure of angle ABW is 25 degrees. This means that the measure of angle CBD is 90-25=65 degrees.
5) In triangle AWB, since angles in a triangle add to 180 degrees, angle BWA measures 130 degrees.
6) Once again, since diagonals of a rectangle are congruent and bisect each other, AW=WD. So, the measures of angles WAD and ADW are each 65 degrees. Thus, because angles in a triangle (in this case triangle AWD) add to 180 degrees, the measure of angle AWD is 50 degrees.
#4(a)
row-seat: 3- 13, 4-15, 5-17, 6-19, 7-21
(b)
the equation works for row 1 but not for any of the rows after this
Ex: Row 2, S=7(2)+2, this would equal 14 but there isn't 14 seats in row #2
(c)
S=2(1)+7, there is 9 seats in row 1
2(2)+7=11, there is 11 seats in row 2
2(3)+7= 13, there is 13 seats in row 3
(d)
2(15)+7=37
2*15=30, 30+7=37
(e)
91=2(r)+7
91-7=2(r)+7-7
84=2(r)
84/2=2(r)/2
42=r, the row with 91 seats is row 42
<span>x-y=2y -> x=3y and
3x-40+2y=180 --> 9y-40+2y=180 --> 11y=220 --> y=20, x=60 --> <A=<C=140 degrees, <B=<D=40 degrees.</span>
