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Question

An illustration shows a triangle with vertices as B C D. Angle C on the top is labeled as a question mark and angle D on the bottom right is labeled as 22 degrees. Vertex B is on the bottom left. The horizontal line D B extends beyond the triangle to the left with an arrow at the end, and a point A is marked on it. The angle of A B C is labeled as 103 degrees.

Use the Triangle Angle Sum Theorem to find the measure of the angle on point C .

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Answer 1

To find the measure of angle C in triangle BCD using the Triangle Angle Sum Theorem, we first recall that this theorem states that the sum of the interior angles of a triangle is always 180 degrees.

Given:

• Angle ACB (angle C) = ? (unknown)
• Angle ADB (angle D) = 22 degrees
• Angle ABC (angle A) = 103 degrees

Using the Triangle Angle Sum Theorem: \[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]

Substituting the known angles into the equation: \[ 103^\circ + 22^\circ + \text{Angle C} = 180^\circ \]

Now, calculate the sum of the known angles: \[ 103^\circ + 22^\circ = 125^\circ \]

Now, we can solve for angle C: \[ 125^\circ + \text{Angle C} = 180^\circ \]

Subtract 125 degrees from both sides: \[ \text{Angle C} = 180^\circ - 125^\circ \] \[ \text{Angle C} = 55^\circ \]

Thus, the measure of angle C is \(55^\circ\).