The diagonals of kite KITE intersect at point P. If / and /, find /. A.
12°
B.
28°
C.
56°
D.
68°

C. 56°

Step-by-step explanation:

In any kite:

1. The intersection of the diagonals of a kite form 90 degree (right) angles

2. Its diagonals are perpendicular

3. The longer diagonal of a kite bisects the shorter one

In Kite KITE

∵ Its two diagonals intersect at point P

∴ KT⊥ IE

∴ m∠KPE = 90°

In ΔKPE

∵ m∠KPE + m∠PEK + m∠PKE = 180° ⇒ interior angles of a triangle

∵ m∠KPE = 90°

∠TKE is the ∠PKE because P ∈ TK

∠IEK is the ∠PEK because P ∈ IE

∵ m∠TKE = (x + 6)°

∴ m∠PKE = (x + 6)°

∵ m∠IEK = (2x)°

∴ m∠PEK = (2x)°

- Substitute the measures of the angles in the rule above

∴ 90 + (2x) + (x + 6) = 180

∴ 90 + 2x + x + 6 = 180

- add like terms in the left hand side

∴ 96 + 3x = 180

- Subtract both sides by 96

∴ 3x = 84

- Divide both sides by 84

∴ x = 28

∵ m∠KEI = (2x)°

∵ x = 28

∴ m∠KEI = 2(28)

∴ m∠KEI = 56°

The measure of angle KEI is 56°

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step-by-step explanation:

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