The measure of angle KEI is 56° ⇒ answer C
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°
Learn more:
You can learn more about perpendicular sides in brainly.com/question/3617539
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