Question
Find ∠DAC in the given figure.
Hint:
We are given a figure. The figure shows a line dividing the angle in two parts. The distance of the line from the sides of the triangle is given same. It is 12. We have given one of the angles. It is 38°. We have to find one of the angles from the figure.
The correct answer is:
The given angle is ∠CAB. The line AD divides the angle.
The angles are ∠DAC and ∠DAB.
∠DAB = 38°.
The distance of the ray from both the sides of angle is CD = 12 and BD = 12.
The distance of the line from both the sides is equal.
This happens when the given line is the angle bisector of the angle.
When a line is angle bisector of the angle, the distance of the line from two sides of the angle is equal.
Angle bisector means the line divides the angle into two equal angles.
So, ∠DAC = ∠DAB
∠DAC = 38°
Therefore, the answer is ∠DAC = 38°.
For such questions, we should know the properties of the angle bisector.
Related Questions to study
Identify the theorem used to solve the problem.
Identify the theorem used to solve the problem.
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For such questions, we should know about the different centers of the circle and triangle.
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For such questions, we should know about the different centers of the circle and triangle.
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Direction : Among given options only for this figure perpendicular bisector theorem is used.
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