Question

which statement about the angles in the figure is true? diagram m∠... + m∠... = 90°; m∠7 + m∠10 = 180°; m∠... + m∠... = 90°; m∠3 + m∠5 = 180°

Explanation:

Step1: Analyze angle relationships

In a triangle, the sum of angles and linear pairs (supplementary angles, \(180^\circ\)) or right angles (\(90^\circ\)) are key. Let's check each option:

• For \(m\angle 3 + m\angle 5\): \(\angle 3\) and \(\angle 5\) are adjacent on a straight line? Wait, no—wait, looking at the figure (a triangle with right angles and intersecting lines), \(\angle 3\) and \(\angle 5\) are adjacent angles forming a linear pair? Wait, no, maybe the first visible correct option: Wait, the option \(m\angle 3 + m\angle 5 = 180^\circ\)? Wait, no, let's re-express. Wait, the figure has a right angle, so maybe the correct one is \(m\angle 3 + m\angle 5 = 180^\circ\)? Wait, no, let's think again. Wait, the first option (partially visible) might be \(m\angle 8 + m\angle 9 = 90^\circ\)? Wait, no, the correct approach: in the triangle, there's a right angle, so angles in a triangle sum to \(180^\circ\), and linear pairs sum to \(180^\circ\). Wait, the option \(m\angle 3 + m\angle 5 = 180^\circ\): \(\angle 3\) and \(\angle 5\) are adjacent on a straight line (linear pair), so their sum is \(180^\circ\). Wait, but let's check other options:

• \(m\angle 7 + m\angle 10 = 180^\circ\): Unlikely, as \(\angle 10\) is a right - related angle.
• The partially visible \(m\angle... + m\angle... = 90^\circ\): Maybe, but the clear linear pair is \(\angle 3\) and \(\angle 5\) (if they are on a straight line). Wait, the correct answer is \(m\angle 3 + m\angle 5 = 180^\circ\) (assuming \(\angle 3\) and \(\angle 5\) form a linear pair, so their measures sum to \(180^\circ\)).

Answer:

\(m\angle 3 + m\angle 5 = 180^\circ\) (the option with this expression)