Question

in the figure, m∠adb. m∠aed = 34° and m∠ead = 112°. find m∠adb m∠adb = °

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle AED\), we know two angles and want to find the third.

Step2: Calculate \(m\angle ADE\)

Let \(m\angle ADE\) be an angle in \(\triangle AED\). Using the angle - sum property \(m\angle AED+m\angle EAD + m\angle ADE=180^{\circ}\). Substitute \(m\angle AED = 34^{\circ}\) and \(m\angle EAD=112^{\circ}\) into the formula: \(34^{\circ}+112^{\circ}+m\angle ADE = 180^{\circ}\). Then \(m\angle ADE=180^{\circ}-(34^{\circ} + 112^{\circ})=180^{\circ}-146^{\circ}=34^{\circ}\).

Step3: Note the linear - pair relationship

\(\angle ADE\) and \(\angle ADB\) form a linear pair. A linear pair of angles is supplementary, so \(m\angle ADE+m\angle ADB = 180^{\circ}\).

Step4: Calculate \(m\angle ADB\)

Since \(m\angle ADE = 34^{\circ}\), then \(m\angle ADB=180^{\circ}-m\angle ADE\). Substitute \(m\angle ADE = 34^{\circ}\) into the formula, we get \(m\angle ADB = 146^{\circ}\).

Answer:

\(146\)