Question

name
geometry ticket 4.1 - 4.3

1. find the measures of the unknown angles

$m\angle abd=$
$m\angle abc=$

Explanation:

Step1: Find \(m\angle ABC\)

Use the triangle - angle sum theorem (\(m\angle A+m\angle C + m\angle ABC=180^{\circ}\)).
Given \(m\angle A = 37^{\circ}\) and \(m\angle C=92^{\circ}\), then \(m\angle ABC=180^{\circ}-(37^{\circ}+92^{\circ})\).

$$m\angle ABC = 180^{\circ}-129^{\circ}=51^{\circ}$$

Step2: Find \(m\angle ABD\)

Use the linear - pair (supplementary angles) relationship (\(m\angle ABC + m\angle ABD=180^{\circ}\)).
Since \(m\angle ABC = 51^{\circ}\), then \(m\angle ABD=180^{\circ}-m\angle ABC\).

$$m\angle ABD=180^{\circ}-51^{\circ}=129^{\circ}$$

Answer:

\(m\angle ABD = 129^{\circ}\), \(m\angle ABC = 51^{\circ}\)