Question

In the diagram of angle ABD shown, Point C is located on BD such that AB is congruent to AC and AC is congruent to CD. If M

Answer 1

Answer

Option B is correct.

Angle ABC = 68°

Explanation

To answer this question, we need to first note that when a triangle has two sides that are equal in length (isoscelles triangle), the base angles of those two sides are often equal to each other.

We also need to note that the sum of angles in a triangle = 180°

And the sum of angles on a straight line = 180°

AB = AC

This means that

Angle ABC = Angle BCA

AC = CD

This means that

Angle CAD = Angle ADC

We are given that Angle ADC = 34°

Angle CAD = Angle ADC = 34° (Base angles of an isoscelles triangle are equal)

So, we can then find the third angle of triangle ACD

Angle ACD + Angle CAD + Angle ADC = 180° (Sum of angles in a triangle)

Angle ACD + 34° + 34° = 180°

Angle ACD + 68° = 180°

Angle ACD = 180° - 68° = 112°

Angle BCA + Angle ACD = 180° (Sum of angles on a straight line)

Angle BCA + 112° = 180°

Angle BCA = 180° - 112°

Angle BCA = 68°

Then, we can easily recall that

Angle ABC = Angle BCA (Base angles of an isoscelles triangle are equal)

Angle ABC = Angle BCA = 68°

Hope this Helps!!!