The measure of arc BEC in circle D is 134°
From the question, we are to determine the measure of arc BEC
Measure of arc BEC = 2 × m∠BAC
First, we will determine the measure of angle ACB
From one of the circle theorems,
The angle subtended by an arc of a circle is twice the angle it subtends anywhere on the circle's circumference
∴ m∠ACB = 1/2 × 76°
m∠ACB = 38°
Then,
m∠BAC + m∠ACB + m∠ABC = 180° (Sum of angles in a triangle)
m∠BAC + 38° + 75° = 180°
m∠BAC + 113° = 180°
m∠BAC = 180°- 113°
m∠BAC = 67°
Then,
Measure of arc BEC = 2 × m∠BAC
Measure of arc BEC = 2 × 67°
Measure of arc BEC = 134°
Hence, the measure of arc BEC is 134°
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