Question

applying the angle addition postulate
in the diagram below, ∠dab and ∠dac are adjacent angles.
if ( mangle dac = 25^circ ), what is ( mangle dab ) in degrees?
what is ( mangle bac ) in degrees?

Explanation:

Step1: Find x using ∠DAC

Given \( m\angle DAC = (x - 20)^\circ = 25^\circ \), solve for \( x \):
\( x - 20 = 25 \)
\( x = 25 + 20 = 45 \)

Step2: Calculate \( m\angle DAB \)

Substitute \( x = 45 \) into \( m\angle DAB = (2x - 10)^\circ \):
\( 2(45) - 10 = 90 - 10 = 80^\circ \)

Step3: Calculate \( m\angle BAC \)

Using the Angle Addition Postulate, \( m\angle BAC = m\angle DAB + m\angle DAC \):
\( 80^\circ + 25^\circ = 105^\circ \)

Answer:

s:

• \( m\angle DAB = \boldsymbol{80^\circ} \)
• \( m\angle BAC = \boldsymbol{105^\circ} \)