what is the measure of angle ABC
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22
Answer:
The size of an angle is measured in degrees (see Angle Measures). When we say 'the angle ABC' we mean the actual angle object. If we want to talk about the size, or measure, of the angle in degrees, we should say 'the measure of the angle ABC' - often written m∠ABC.
Angle ABC is a straight angle, or 180°.
Answered by
7
Given:
∠BAD = 30°
AB = AD
∠BCD = 60°
BC = CD
To find: ∠ABC
Calculation:
In ΔABD,
∠A + ∠B + ∠D = 180°
And since AB = AD, so ∠B = ∠D
Let ∠B = ∠D = p
Therefore, ∠A + ∠B + ∠D = 180°
30° + p + p = 180°
2p = 150°
p = 75° hence ∠ABD = 75°
In ΔBCD:
∠B + ∠C + ∠D = 180°
∠B + 60° + ∠D = 180°
Let ∠B = ∠D = x,
So, x + 60° + x = 180°
60° + 2x = 180°
x = 60° hence ∠CBD = 60°
∠ABC = ∠ABD - ∠CBD = 75° - 60° = 15°
Answer:
The value of ∠ABC = 15°.
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