Question

Measure of angle 3 equals 37. find measure of angle 1. a pair of intersecting lines is shown. angle 1 is above the point of intersection. angle 2 is right of the point of intersection. angle 3 is below the point of intersection. angle 4 is left of the point of intersection. 37

143
127
153

Answer 1

The measure of angle 1 is 143 degrees.

Step-by-step explanation:

In this case, we're dealing with intersecting lines, forming angles that obey specific rules. When two lines intersect, opposite angles are equal. Hence, angle 3, given as 37 degrees, is equal to angle 1. Moreover, angles 1 and 2 form a straight line (180 degrees), making angle 1 supplementary to angle 2. As angle 2 is not directly specified, we can use its relationship with angle 3 to find angle 1. Angle 2 and angle 3 together form a straight line, totaling 180 degrees. Therefore, angle 2 is 143 degrees (180 - 37 = 143), making angle 1, which is equal to angle 3, also 143 degrees.

In detail, given that angle 3 equals 37 degrees and angles 3 and 2 form a straight line, their sum equals 180 degrees (angle 3 + angle 2 = 180). Therefore, angle 2 = 180 - 37 = 143 degrees. As angles 1 and 2 are supplementary, their sum equals 180 degrees. Hence, angle 1 = 180 - 143 = 37 degrees. However, it's essential to recognize the relationship between angle 1 and angle 3 due to their position and intersection. According to the properties of intersecting lines, angle 1 is equal to angle 3. Thus, angle 1 = 37 degrees, matching the given measure of angle 3.

Understanding the properties of intersecting lines and their associated angles is crucial in solving this problem. By applying the rule that vertical angles (opposite angles) are equal, we establish the relationship between angles 1 and 3. Moreover, recognizing the supplementary nature of angles forming a straight line (180 degrees) helps us find the missing angle (angle 2) and subsequently deduce the measure of angle 1.

Answer 2

The measure of angle 1 is a) 37 degrees.

To find the measure of angle 1, we need to understand the relationship between angle 1 and angle 3 in an intersecting line. When two lines intersect, the opposite angles are equal. In other words, angle 1 is equal to angle 3. Since angle 3 is given as 37 degrees, angle 1 is also 37 degrees.

In Mathematics, when two lines intersect, they form four angles at the point of intersection. The angles opposite to each other (called vertical angles) are always equal. Because angle 1 and angle 3 are vertical angles, they are equal in measurement. Therefore, if the measure of angle 3 is 37 degrees, then the measure of angle 1 is also 37 degrees.