Question
In Exercises 17-20 find the measures of angle X and angle Y. (See Example 4.) 18. w. 17.
Answer
4.1
(245 Votes)
Neil
Advanced · Tutor for 1 years
Answer
To find the measures of
and
in the quadrilateral XYZW, we need to use the information provided in the picture details. Let's go through the steps to solve for these angles.Step 1: Analyze the given informationWe know that:-
-
-
is a right angle, so
-
is a right angle, so
Step 2: Use the properties of quadrilateralsThe sum of the interior angles of any quadrilateral is 360°. Therefore, we can write the following equation:
Step 3: Find
and
Since
and
are adjacent angles that form a straight line, their sum is 180°. Therefore:
Similarly, since
and
are adjacent angles that form a straight line, their sum is also 180°. Therefore:
Step 4: Substitute
and
into the quadrilateral angle sum equationNow we can substitute the values of
and
into the quadrilateral angle sum equation:
Step 5: Solve for
Step 6: Find
and
We cannot determine the exact measures of
and
with the given information alone because there are multiple possibilities for their measures that would add up to 266°. Additional information, such as the lengths of the sides or other angle measures, would be necessary to find the exact measures of
and
.Final Answer:Without additional information, we can only determine that the sum of
and
is 266°. The exact measures of
and
cannot be determined from the given information.