Question

in the diagram, ∠dab and ∠dac are adjacent angles. if m∠dac = 25°, what is m∠dab in degrees? what is m∠bac in degrees? 105 100 85 80 < 80 <

Explanation:

Step1: Set up equation for adjacent - angles

Since \(\angle DAB\) and \(\angle DAC\) are adjacent angles, \(\angle BAC=\angle DAB + \angle DAC\), so \((2x - 10)+(x - 20)\).

Step2: Simplify the expression

\((2x - 10)+(x - 20)=2x-10+x - 20=3x-30\).

Step3: Solve for \(x\) if \(\angle DAC = 25^{\circ}\)

If \(x - 20=25\), then \(x = 45\).

Step4: Find \(\angle DAB\)

Substitute \(x = 45\) into \(\angle DAB=2x - 10\), we get \(2\times45-10=90 - 10 = 80^{\circ}\).

Answer:

80