Question

kite fgh k is shown. what is the value of m? (diagram: kite with vertices f, g, h, k; side ( gh ) labeled ( 5m + 1 ), side ( kh ) labeled ( 3m + 7 ).) multiple - choice options: ( m = 2 ), ( m = 3 ), ( m = 15 ), ( m = 16 ).

Explanation:

Step1: Recall kite properties

In a kite, two pairs of adjacent sides are equal. So, \( GH = KH \), which means \( 5m + 1 = 3m + 7 \).

Step2: Solve for m

Subtract \( 3m \) from both sides: \( 5m - 3m + 1 = 7 \) → \( 2m + 1 = 7 \).
Subtract 1 from both sides: \( 2m = 7 - 1 \) → \( 2m = 6 \).
Divide by 2: \( m = \frac{6}{2} = 3 \).

Answer:

\( m = 3 \) (corresponding to the option "m=3")