![]() ![]() Next, we must set the two expressions 180 – A and 2(90 – A) + 40 equal to one another and solve for A: The problem states that the measure of the supplement of A is 40 degrees larger than twice the measure of the complement of A. ![]() Similarly, because the sum of the measures of angle A and its supplement is 180 degrees, we can represent the measure of the supplement of A as 180 – A. We can write the following equation to determine an expression for the measure of the complement of angle A. By definition, the sum of the measures of A and its complement is 90 degrees. Let A represent the measure, in degrees, of angle A. Now, we can substitute 36 as the value of x and then solve for z. Because the sum of the measure of an angle and the measure of its complement equals 90, we can write the following equation: However, the original question asks us to find the measure of the complement of ABC, which we denoted previously as z. Multiply both sides by 2 to get rid of the fraction. Next, we can substitute this value into the equation (1/2)y = 2x and then solve for x. We could write this equation as follows:īecause x + y = 180, we can solve for y in terms of x by subtracting x from both sides. We are told that one-half of the measure of the supplement is equal to twice the measure of ABC. Let x equal the measure of angle ABC, let y equal the measure of the supplement of angle ABC, and let z equal the measure of the complement of angle ABC.īecause x and y are supplements, the sum of their measures must equal 180. ![]()
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