A kite WXYZ has diagonals WY and XZ that intersect at point P. If the length of WP is 4 ce… — ACT

A kite $WXYZ$ has diagonals $WY$ and $XZ$ that intersect at point $P$ . If the length of $WP$ is $4$ centimeters, the length of $PY$ is $9$ centimeters, and the length of $XP$ is $3$ centimeters, what is the measure, in degrees, of angle $WPX$ ?

A
30
B
45
C
60
90Answer
E
180

Answer

90 degrees

The diagonals of a kite are always perpendicular to each other. Therefore, the angle formed at their intersection, angle

WPX

, is a right angle, which measures exactly

90

degrees. The given segment lengths are extra information.

Step-by-Step Solution

Identify the fundamental property of the diagonals of a kite.

The diagonals of any kite are perpendicular to each other.

By geometric definition, the diagonals of a kite intersect at a right angle.

Determine the measure of the angle formed by the intersection of the diagonals.

Angle

WPX

is a right angle, which measures exactly

90

degrees.

Since the diagonals are perpendicular, their intersection forms four

90

-degree angles regardless of the lengths of the individual diagonal segments.

Key Concept

The diagonals of a kite are perpendicular (

90^\circ

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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