Question

find ∠adb, if the measure of ∠adc is 123°. draw

Explanation:

Step1: Set up angle sum equation

Since $\angle ADC = \angle ADB + \angle BDC$, we have $(2a + 74) + (a + 46) = 123$.

Step2: Solve for \(a\)

Combine like terms: \(3a + 120 = 123\). Subtract 120: \(3a = 3\), so \(a = 1\).

Step3: Find \(\angle ADB\)

Substitute \(a = 1\) into \(\angle ADB = (2a + 74)^\circ\): \(2(1) + 74 = 76\).

Answer:

\(76^\circ\)