Question

1. given: bd bisects ∠abc

∠abd=(5x + 30)°
∠dbc=(10x + 5)°
find: m∠abd

1. solve for x and name the angle relationship.

40° (12x - 8)°

1. solve for y and name the angle relationship.

78° (5y + 2)°

1. what is the complement of 41°?
2. what is the supplement of 73°?

Explanation:

21.

Step1: Use angle - bisector property

Since \(BD\) bisects \(\angle ABC\), then \(\angle ABD=\angle DBC\). So we set up the equation \(5x + 30=10x+5\).

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Step2: Find \(m\angle ABD\)

Substitute \(x = 5\) into the expression for \(\angle ABD\). \(\angle ABD=(5x + 30)^{\circ}\), so \(\angle ABD=(5\times5+30)^{\circ}=(25 + 30)^{\circ}=55^{\circ}\)

Step1: Identify angle - relationship

The angles \(40^{\circ}\) and \((12x - 8)^{\circ}\) are vertical angles. Vertical angles are equal. So we set up the equation \(12x-8 = 40\).

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Step2: Name the angle - relationship

The angle - relationship is vertical angles.

Step1: Identify angle - relationship

The angles \(78^{\circ}\) and \((5y + 2)^{\circ}\) are vertical angles. Since vertical angles are equal, we set up the equation \(5y+2=78\).

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Step2: Name the angle - relationship

The angle - relationship is vertical angles.

Answer:

\(55^{\circ}\)

22.