Questions: Statements 1) angle ABC and angle CBD are a linear pair. 2) m angle ABC + m angle CBD = m angle ABD 3) m angle ABD = 180 Reasons 1) Given 2) Angle Addition Postulate 3) Definition of straight angles

Statements
1) angle ABC and angle CBD are a linear pair.
2) m angle ABC + m angle CBD = m angle ABD
3) m angle ABD = 180

Reasons
1) Given
2) Angle Addition Postulate
3) Definition of straight angles

Transcript text: Statements 1) $\angle A B C$ and $\angle C B D$ are a linear pair. 2) $\mathrm{m} \angle A B C+m \angle C B D=m \angle A B D$ 3) $m \angle A B D=180$ Reasons 1) Given 2) Angle Addition Postulate 3) Definition of straight angles

Solution

Solution Steps

The given problem appears to be a proof involving angles and their properties. Let's outline the solution approach for the first three statements:

Identify the given information: $\angle ABC$ and $\angle CBD$ are a linear pair.
Use the Angle Addition Postulate: The sum of the measures of $\angle ABC$ and $\angle CBD$ is equal to the measure of $\angle ABD$.
Apply the definition of a straight angle: The measure of $\angle ABD$ is 180 degrees.

Step 1: Identify the Given Information

We are given that $\angle ABC$ and $\angle CBD$ are a linear pair. This means that these two angles are adjacent and their non-common sides form a straight line.

Step 2: Apply the Angle Addition Postulate

According to the Angle Addition Postulate, the sum of the measures of $\angle ABC$ and $\angle CBD$ is equal to the measure of $\angle ABD$: \[ m \angle ABC + m \angle CBD = m \angle ABD \]

Step 3: Use the Definition of a Straight Angle

A straight angle is defined as an angle that measures $180^\circ$. Therefore, we can state: \[ m \angle ABD = 180^\circ \]

Step 4: Substitute the Given Angle Measures

Given that $m \angle ABC = 90^\circ$ and $m \angle CBD = 90^\circ$, we substitute these values into the equation from Step 2: \[ 90^\circ + 90^\circ = m \angle ABD \]

Step 5: Calculate the Measure of $\angle ABD$

Perform the addition: \[ m \angle ABD = 180^\circ \]

Step 6: Verify if $\angle ABD$ is a Straight Angle

Since $m \angle ABD = 180^\circ$, $\angle ABD$ is indeed a straight angle.