Question

m ∠1 = 40 50 130 (diagram includes angles 90°, 40°, 90° and a right triangle with angle 1)

Explanation:

Step1: Identify right triangle angle sum

In a right triangle, the sum of angles is \(180^\circ\), and one angle is \(90^\circ\). So the other two angles sum to \(180^\circ - 90^\circ = 90^\circ\).

Step2: Use vertical/alternate angles

The \(40^\circ\) angle and the angle complementary to \(\angle 1\) are equal (vertical or alternate interior angles). Let the angle complementary to \(\angle 1\) be \(x\), so \(x = 40^\circ\).

Step3: Calculate \(\angle 1\)

Since \(\angle 1 + x = 90^\circ\) (from right triangle), substitute \(x = 40^\circ\): \(\angle 1 = 90^\circ - 40^\circ = 50^\circ\).

Answer:

\(50\) (corresponding to the option with value 50)