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

The temperature at 4 a.m. was -13 °F. The temperature was rising at a steady rate of 5°F an hour. At what time will the temperat

Dovator [93]

At 9 a.m. the temperature will be 12

7 0

3 years ago

A scale distance of 3 centimeters on a map represents an actual distance of 51 feet.

Rom4ik [11]

In this case, the best way to work this out is to find what 1cm is equal to. In this case, you have to divide 51/3, giving you 17. You know that 17 feet. You can now divide 187/17, giving you 11. Therefore, 11cm is equal to 187 feet. Hope this helps

8 0

3 years ago

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