Question

PLS HELP me!!!!!!!!!!!!!!!!!!!!11

Answer 1

The measure of the angle ∠ABC is 108°

Explanation:

An isosceles triangle has two equal sides and two equal angles

In this problem

∠BDA=∠BAD= 66° ----> the angles of the base are equals

Find the measure of the vertex angle

∠ABD = 180° - 2×66° = 48° (the sum of the internal angles of a triangle is equal to 180°)

then. Find the measure of the angle ∠CBD in the equilateral triangle we know that

The measure of the internal angle in a equilateral triangle is 60° so

∠CBD= 60°

Then find the measure of the angle ∠ABC

∠ABC=∠ABD+∠DBC

substitute the values

∠ABC= 48°+60° = 108°

The answer is 108°

The measure of the angle ∠ABC is 108°

Answer 2

108 degrees

Explanation:

Hi there!

1. Determine the measure of angle DBC

2. Determine the measure of angle ABD

3. Add them to determine the measure of angle ABC

We're given that triangle ABD is isosceles and triangle BCD is equilateral.

Because BCD is an equilateral triangle, all of its interior angles at 60 degrees.

Therefore, the measure of angle DBC is 60 degrees.

Triangle ABD is isosceles, so therefore, angle ADB is also 66 degrees.

The sum of the interior angles of a triangle is 180 degrees. Therefore, the measure of angle ABD is 180-66-66, which is 48 degrees.

To find ABC, add 60 and 48:

60+48 = 108

Therefore, angle ABC measures 108 degrees.

I hope this helps!