Question

1. finish the equation: ( mangle3 + 37^{circ}=)____(^{circ})

a. 180
b. 90
c. 360
d. 45
what is the measure of angle 3?

Explanation:

Step1: Analyze the angle relationship

Assume that \(\angle3\) and \(37^{\circ}\) form a right - angle. In a right - angle, the sum of two complementary angles is \(90^{\circ}\).

Step2: Check each option

• Option A: If \(m\angle3 + 37^{\circ}=180^{\circ}\), then \(\angle3\) and \(37^{\circ}\) are supplementary angles. But there is no indication in the problem (from the context of the question about basic angle relationships likely in a geometry chapter on basic angles) that they are supplementary.
• Option B: If \(m\angle3 + 37^{\circ}=90^{\circ}\), then \(\angle3\) and \(37^{\circ}\) are complementary angles. This is a common relationship taught in basic geometry for angles that form a right - angle.
• Option C: If \(m\angle3+37^{\circ} = 360^{\circ}\), this would imply a full - circle relationship which is not relevant for two non - overlapping angles in a basic angle - relationship problem.
• Option D: \(45^{\circ}\) is an arbitrary value. Since \(37^{\circ}+45^{\circ}=82^{\circ}

eq90^{\circ}\), \(180^{\circ}\), or \(360^{\circ}\) (except for the wrong sum \(82^{\circ}\)) and there is no basis for this sum.

Step3: Calculate \(m\angle3\)

If \(m\angle3 + 37^{\circ}=90^{\circ}\), then \(m\angle3=90^{\circ}- 37^{\circ}\).

$$m\angle3=53^{\circ}$$

Answer:

1. B. \(90\)

The measure of angle \(3\) is \(53^{\circ}\)