Question

so how do you draw the angle abc meassures 65

Answer 1

ok Q. Find the m angle ADB in the given ΔABC, if AD is the angle bisector of angle BAC and if m angle ABC = 75 and m angle BCA = 65
Choices are:
a. 65
b. 85
c. 75
d. 55

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Answers
Answer 1
m angle ABC = 75 and m angle BCA = 65 [Given.]

The sum of the measures of the angles of a triangle is 180. [Triangle -Angle sum theorem.]

So, m angle BAC + m angle ABC + m angle BCA = 180

m angle BAC + 75 + 65 = 180 [Substitute given measures.]

m angle BAC = 180 - 140 = 40

AD is the angle bisector of angle BAC [Given.]

So, m angle BAD = m∠BAC/2 = 40/2 = 20

The sum of the measures of the angles of a triangle is 180. [Triangle angle sum theorem.]

m angle BAD + m angle ABD + m angle ADB = 180

20 + 75 + m angle ADB = 180 [Substitute given measures.]

m angle ADB = 180 - 95 = 85

Thus, correct answer is option 'B'.

Answer 2

Q. Find the m angle ADB in the given ΔABC, if AD is the angle bisector of angle BAC and if m angle ABC = 75 and m angle BCA = 65
Choices are:
a. 65
b. 85
c. 75
d. 55


m angle ABC = 75 and m angle BCA = 65 [Given.]

The sum of the measures of the angles of a triangle is 180. [Triangle -Angle sum theorem.]

So, m angle BAC + m angle ABC + m angle BCA = 180

m angle BAC + 75 + 65 = 180 [Substitute given measures.]

m angle BAC = 180 - 140 = 40

AD is the angle bisector of angle BAC [Given.]

So, m angle BAD = m∠BAC/2 = 40/2 = 20

The sum of the measures of the angles of a triangle is 180. [Triangle angle sum theorem.]

m angle BAD + m angle ABD + m angle ADB = 180

20 + 75 + m angle ADB = 180 [Substitute given measures.]

m angle ADB = 180 - 95 = 85

Thus, correct answer is option 'B'.