Question

the measure of \\(\angle dab\\) equals 125°. the measure of \\(\angle acb\\) equals 30°. what is \\(m\angle abc\\)? enter your answer in the box.

Explanation:

Step1: Find ∠BAC

Since ∠DAB is 125°, and ∠DAB and ∠BAC are supplementary (they form a linear pair), we use the formula \( \angle BAC = 180^\circ - \angle DAB \).
\( \angle BAC = 180^\circ - 125^\circ = 55^\circ \)

Step2: Use Triangle Angle Sum

In triangle \( ABC \), the sum of interior angles is \( 180^\circ \). We know \( \angle BAC = 55^\circ \) and \( \angle ACB = 30^\circ \). Let \( \angle ABC = x \). Then:
\( \angle BAC + \angle ACB + \angle ABC = 180^\circ \)
\( 55^\circ + 30^\circ + x = 180^\circ \)
\( 85^\circ + x = 180^\circ \)
\( x = 180^\circ - 85^\circ = 95^\circ \)

Answer:

\( 95^\circ \)