Question

use the triangle angle sum theorem to find the measure of the angle on point C. CBD makes a triangle. Angle ABD makes a supplementary line. Angle B is unknown. Angle D is 22 degrees. Angle A is 103 degrees

Answer 1

To find the measure of angle C in triangle ABD, we can use the triangle angle sum theorem, which states that the sum of the angles in a triangle is \(180\) degrees.

In triangle ABD, we have the following:

- Angle A = \(103\) degrees
- Angle D = \(22\) degrees
- Angle B = unknown

According to the triangle angle sum theorem:

\[
\text{Angle A} + \text{Angle B} + \text{Angle D} = 180
\]

Plugging in the known values:

\[
103 + \text{Angle B} + 22 = 180
\]

Now combine the known angles:

\[
125 + \text{Angle B} = 180
\]

To find angle B, subtract \(125\) from both sides:

\[
\text{Angle B} = 180 - 125 = 55 \text{ degrees}
\]

Thus, angle B measures \(55\) degrees.

If point C refers to the angle formed by extending line BD, then angle C will be:

\[
\text{Angle C} = 180 - \text{Angle B}
\]

Since angle B is \(55\) degrees:

\[
\text{Angle C} = 180 - 55 = 125 \text{ degrees}
\]

Therefore, the measure of angle C is \(125\) degrees.