Question

the sum of the measures of complementary angles is 90°. the measure of angle m is (4x)°. the measure of angle n is 42°. angle m and angle n are complementary. find the value of x. the sum of the measures of supplementary angles is 180°. the measure of angle j is (2y - 3)°. the measure of angle k is 73°. angle j and angle k are supplementary. what is the value of y? two complementary angles have measures (z + 2)° and (3z)°. determine the value of z. use the diagram to find the value of w.

Explanation:

Step1: Recall complementary - angles property

Complementary angles sum to 90°. For angle M = (4x)° and angle N = 42°, we have the equation 4x+42 = 90.

Step2: Solve for x

Subtract 42 from both sides of the equation: 4x=90 - 42. So, 4x = 48. Then divide both sides by 4: x = $\frac{48}{4}$ = 12.

Step3: Recall supplementary - angles property

Supplementary angles sum to 180°. For angle J=(2y - 3)° and angle K = 73°, we have the equation (2y - 3)+73 = 180.

Step4: Simplify the equation for y

Combine like - terms: 2y+70 = 180. Subtract 70 from both sides: 2y=180 - 70 = 110. Then divide both sides by 2: y = $\frac{110}{2}$ = 55.

Step5: Solve for z for complementary angles

For complementary angles (z + 2)° and (3z)°, we have the equation (z + 2)+3z = 90. Combine like - terms: 4z+2 = 90. Subtract 2 from both sides: 4z=88. Divide both sides by 4: z = 22.

Step6: Solve for w

For the angles (5w - 4)° and 46°, if they are complementary (assuming from the context of angle - solving), we have the equation (5w - 4)+46 = 90. Combine like - terms: 5w+42 = 90. Subtract 42 from both sides: 5w=48. Divide both sides by 5: w = $\frac{48}{5}$ = 9.6.

Answer:

x = 12, y = 55, z = 22, w = 9.6