Question

10 triangle oef is shown. what is the measurement of \\( \angle oef \\)? 140 degrees 40 degrees 60 degrees 100 degrees close all

Explanation:

Step1: Find the adjacent angle to 140°

A straight line is 180°, so the angle adjacent to 140° in triangle DEF (at point F) is \( 180^\circ - 140^\circ = 40^\circ \).

Step2: Use triangle angle sum property

The sum of angles in a triangle is \( 180^\circ \). In triangle OEF (assuming O, E, F are vertices), we know one angle is \( 100^\circ \) (at O) and another is \( 40^\circ \) (at F). Let \( \angle OEF = x \). Then \( 100^\circ + 40^\circ + x = 180^\circ \).
Solving for \( x \): \( x = 180^\circ - 100^\circ - 40^\circ = 40^\circ \)? Wait, no, maybe I misread. Wait, the angle at O is 100°, the angle at F (inside triangle) is 40°, so angle at E (∠OEF) is \( 180 - 100 - 40 = 40 \)? Wait, but the options have 40 degrees. Wait, let's recheck.

Wait, the exterior angle at F is 140°, so interior angle at F is 180 - 140 = 40°. Then in triangle OEF, angles are 100° (at O), 40° (at F), so angle at E (∠OEF) is 180 - 100 - 40 = 40°. So the measure of ∠OEF is 40 degrees.

Answer:

40 degrees (the option with 40 degrees)