The measure of angle CKB (m ∠CKB) is 144°
Calculating angles
From the question, we are to determine the measure of angle CKB (m ∠CKB)
First, we will determine the value of x
From the given information,
m ∠KAE = 3x
m ∠KCD = 2x
In the diagram,
m ∠KCD = m ∠AKE (Alternate angles)
∴ m ∠AKE = 2x
Also,
m ∠KAE + m ∠AKE + m ∠AEK = 180° (Sum of angles in a triangle)
3x + 2x + 90° = 180°
5x = 180° - 90°
5x = 90°
x = 90°/5
x = 18°
But,
m ∠CKB = 180° - m ∠AKE (Sum of angles on a line segment)
m ∠CKB = 180° - 2x
m ∠CKB = 180° - 2(18°)
m ∠CKB = 180° - 36°
m ∠CKB = 144°
Hence, the measure of angle CKB (m ∠CKB) is 144°
Learn more on Calculating measure of angles here: https://brainly.com/question/18359073
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