The measure of angle, m∠BDC is 43°
The reason for the above value is as follows;
The angles of known measures and parameters of the circle are;
m∠ADB = 43°
m∠AOB = m∠BOC
The required parameter;
The measure of angle m∠BDC
Method:
Apply circle theory; The measure of the angle subtended by an arc at the center is twice the angle subtended at the circumference.
Based on the above theory, we have;
The angle subtended by the arc AB at the center = m∠AOB
The angle subtended by the arc AB at the circumference = m∠ADB
Therefore, m∠AOB = 2 × m∠ADB
Which gives:
m∠AOB = 2 × 43° = 86°
m∠AOB = 86°
m∠AOB = m∠BOC
∴ m∠BOC = m∠AOB = 86°
m∠BOC = 86°
Similarly, based on circle theory, we have:
The angle subtended by the arc BC at the center = m∠BOC
The angle subtended by the arc BC at the circumference = m∠BDC
Therefore:
m∠BOC = 2 × m∠BDC
m∠BDC = (m∠BOC)/2
∴ m∠BDC = 86°/2 = 43°
The measure of angle, m∠BDC = 43°.
Learn more about circle theorem here;
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