Question

find the m∠bac, if m∠dec = 58° and m∠edc = 43°. options: 79°, 101°, 58°, 43°. diagram shows points a, c, e on a line, triangles abc and cde with ab || cd, bc || de.

Explanation:

Step1: Find ∠DCE in △DEC

In a triangle, the sum of interior angles is \(180^\circ\). So, \(m\angle DCE = 180^\circ - m\angle DEC - m\angle EDC\).
Substitute \(m\angle DEC = 58^\circ\) and \(m\angle EDC = 43^\circ\):
\(m\angle DCE = 180^\circ - 58^\circ - 43^\circ = 79^\circ\).

Step2: Use parallel lines to find ∠BAC

Since \(\overline{AB} \parallel \overline{CD}\) and \(\overline{AC}\) is a transversal, \(\angle BAC\) and \(\angle DCE\) are alternate interior angles. Alternate interior angles are equal when lines are parallel.
So, \(m\angle BAC = m\angle DCE = 79^\circ\).

Answer:

\(79^\circ\)