Question

Use the properties of angle measures to find the measure of each marked angle. a = (x + 65)° b = (x + 51)° 74°, 74°, 32° 16°, 32°, 132° 32°, 81°, 67° 16°, 32°, 42°.

a) x = 43° , b = 102°
b) x = 13° , b = 83°
c) x = 28° , b = 58°
d) x = 11° , b = 62°

Answer 1

To find the measure of each marked angle, we need to set up equations based on the given angle measures and use the properties of angle measures to solve for the unknown variables.

Step-by-step explanation:

To find the measure of each marked angle, we can use the properties of angle measures. Given that angle a is equal to (x + 65)° and angle b is equal to (x + 51)°, we can set up equations based on the given angle measures: a = 74°. b = 74°. a + b + 32° = 180° (sum of angles in a triangle). From equation (1), we have (x + 65)° = 74°. Solving for x, we get x = 74° - 65° = 9°. Substituting the value of x into equation (2), we have (x + 51)° = 74°. Solving for x, we get x = 74° - 51° = 23°. Therefore, the measure of angle a is (x + 65)° = 9° + 65° = 74° and the measure of angle b is (x + 51)° = 23° + 51° = 74°.