Answer:
x = , y = 6
Step-by-step explanation:
5x + y = 7 → (1)
20x + 2 = y → (2)
Substitute y = 20x + 2 into (1)
5x + 20x + 2 = 7
25x + 2 = 7 ( subtract 2 from both sides )
25x = 5 ( divide both sides by 25 )
x = =
Substitute this value into (2) and evaluate
20( ) + 2 = y
4 + 2 = y , so
y = 6
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.