Question

what is m∠2 + m∠3? explain.
a. 180; m∠1 + 90 = 180, so m∠2 + m∠3 = 180.
b. 180; m∠1 + 90 = m∠2 + m∠3, so m∠2 + m∠3 = 180.
c. 90; m∠1 + m∠2 + m∠3 = 180, m∠1 = 90, so m∠2 + m∠3 = 90.
d. 90; ∠2 and ∠3 are corresponding angles, so m∠2 + m∠3 = 90.

Explanation:

Step1: Identify angle - sum property

The sum of angles in a triangle formed by the intersection of the lines is 180 degrees. Here, considering the triangle with angles ∠1, ∠2, and ∠3, we know that \(m\angle1 + m\angle2 + m\angle3=180^{\circ}\).

Step2: Determine the measure of ∠1

From the figure, we can see that ∠1 is a right - angle, so \(m\angle1 = 90^{\circ}\).

Step3: Solve for \(m\angle2 + m\angle3\)

Substitute \(m\angle1 = 90^{\circ}\) into the equation \(m\angle1 + m\angle2 + m\angle3 = 180^{\circ}\). We get \(90^{\circ}+m\angle2 + m\angle3 = 180^{\circ}\). Then, by subtracting 90 from both sides of the equation: \(m\angle2 + m\angle3=180 - 90=90^{\circ}\).

Answer:

D. 90; \(m\angle1 + m\angle2 + m\angle3 = 180\), \(m\angle1 = 90\), so \(m\angle2 + m\angle3 = 90\)