Applying the triangle sum theorem, the size of ∠BDC = 95°.
What is the Triangle Sum Theorem?
All three interior angles of any triangle have a sum that equals 180 degrees, based on the triangle sum theorem.
The diagram attached below shows the following:
- m∠BAD = 55°
- m∠BCD = 25°
- m∠ABD = 2x°
- m∠CBD = 3x°
Thus:
55 + 2x + 3x + 25 = 180 (triangle sum theorem).
80 + 5x = 180
5x = 180 - 80
5x = 100
x = 20
Therefore,
m∠BDC = 180 - (3x + 25) (triangle sum theorem)
m∠BDC = 180 - (3(20) + 25)
m∠BDC = 95°
Therefore, applying the triangle sum theorem, the size of ∠BDC = 95°.
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