Question

in the diagram below, ∠dab and ∠dac are adjacent angles.
if ( mangle dac = 25^circ ), what is ( mangle dab ) in degrees?
80
what is ( mangle bac ) in degrees?
80
85
100
105

Explanation:

Step1: Find x using ∠DAC

We know that \( m\angle DAC = 25^\circ \), and \( \angle DAC=(x - 20)^\circ \). So we set up the equation:
\( x-20 = 25 \)
Adding 20 to both sides:
\( x=25 + 20=45 \)

Step2: Find \( m\angle DAB \)

We know \( \angle DAB=(2x - 10)^\circ \), substitute \( x = 45 \):
\( 2(45)-10=90 - 10 = 80^\circ \) (which matches the given value for \( m\angle DAB \))

Step3: Find \( m\angle BAC \)

\( \angle BAC=\angle DAB+\angle DAC \)
We know \( \angle DAB = 80^\circ \) and \( \angle DAC = 25^\circ \), so:
\( \angle BAC=80 + 25=105^\circ \)

Answer:

\( m\angle BAC = 105^\circ \) (the option is 105)