Triangle ABC is isosceles, with AB = AC.
Angle ACD = 113°
Work out the size of angle BAC
Answers
Answer:
AC = BC ( given)
=> <A = <B = 2x ( angles opposite to equal sides of a triangle)
< A is bisected to x
AD = AB ( given)
=> < ADB = < ABD = 2x
In triangle ACD,
exterior angle ADB = <CAD + < ACD
SO, < ACD = 2x - x = x
Now, in triangle ABC
x + 2x + 2x = 180° ( angle sum property of a triangle)
= 5x = 180°
=> x = 180/5 = 36°
< ACB = 36°…….ANS
In triangle ABC, AC = BC
that gives us angle(BAC) = angle (ABC) = A
In triangle ABD, AD = AB
that give us angle (ABD) = angle(ADB)
also angle (ABD) = angle (ABC) = A = angle (ADB) - from above relations.
In triangle ABD,
angle(ABD) = angle (ADB) = A and angle (BAD) = A/2, since AD is angular bisector.
Sum of angles = 180
A + A + A/2 = 180
A = 72.
In triangle ABC, angle (ABC) = angle (BAC) = A and angle (BCA) = C
A + A + C = 180
C = 180 - 2(72) = 36.
C = 36 degrees.
Given AC = BC. Then angles B and A are equal. Let them be equal to 2x.
AD bisects angle A. Then angle BAD = x
Given that AD = AB, in triangle BAD,,angles ADB and DBA are equal.
Angle DBA is angle B = 2x. Then, in triangle BAD, the sum of all the three angles (BAD + ADB + DBA = x + 2x + 2x) = 5x = 180 Or x=36 degree
In the triangle,angles B and A equal 2x = 72 degree
Thus, angle ACB = 36 degrees
Step-by-step explanation:
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AC = BC ( given)
=> <A = <B = 2x ( angles opposite to equal sides of a triangle)
< A is bisected to x
AD = AB ( given)
=> < ADB = < ABD = 2x
In triangle ACD,
exterior angle ADB = <CAD + < ACD
SO, < ACD = 2x - x = x
Now, in triangle ABC
x + 2x + 2x = 180° ( angle sum property of a triangle)
= 5x = 180°
=> x = 180/5 = 36°
< ACB = 36°…….ANS