To find: the values of x and y for a given parallelogram.
Answer to Problem 21WE
The value of x is
The value of y is
Explanation of Solution
Given information:
A diagram representing a parallelogram with its
Formula used:
1) By theorem 5-2, the opposite angles of a parallelogram are in congruence with each other, which imply their measures being equal.
2) The sum of the angles of a
Calculation:
Consider the figure given below.
Based on the Theorem 5-2, it can be said that the opposite angles of the given parallelogram has the same value. This can be expressed as
Now, by using the property of sum of angles in ΔACD
Similarly, the sum of angles in ΔABC can be expressed as,
Substituting the value of x in equation (1) the equation can be rewritten as follows.
Substituting the value of
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