Final answer:
The measure of angle ZCIJ is found to be 130 degrees by first finding the value of x using the supplementary angles on a straight line and then substituting that value into the expression for m∠ZCIJ.
Step-by-step explanation:
The student asks to find the measure of angle ZCIJ given that the measure of angle HIJ is 175°, the measure of angle ZHIC is x + 30, and the measure of angle ZCIJ is x + 155.
To find the measure of angle ZCIJ, we need to understand that angles HIJ and HIC are supplementary if they are on a straight line, meaning their measures add up to 180°. Therefore, we can write the following equation:
m∠HIJ + m∠HIC = 180°
Substitute the given values:
175° + (x + 30) = 180°
Now, solve for x:
x + 205° = 180°
x = 180° - 205°
x = -25°
Finally, plug the value of x into the expression for m∠ZCIJ:
m∠ZCIJ = x + 155 = -25° + 155° = 130°
The measure of angle ZCIJ is 130°.