To solve this question, let's follow the given information step by step:
We are given that ZC and ZD are supplementary angles, which means that the sum of angles ZC and ZD is 180° because supplementary angles add up to 180°.
1. We know the measure of angle C (ZC) is 128°.
2. We’re told that the measure of angle D (ZD) is twice the value of x, so ZD = 2x.
Since angles ZC and ZD are supplementary, their measures must add up to 180°.
So the equation based on the given information is:
[tex]\( \text{measure of angle C} + \text{measure of angle D} = 180° \)[/tex]
[tex]\( 128° + 2x = 180° \)[/tex]
Now we'll solve for x:
[tex]\( 2x = 180° - 128° \)[/tex]
[tex]\( 2x = 52° \)[/tex]
Divide both sides by 2 to solve for x:
[tex]\( x = \frac{52°}{2} \)[/tex]
[tex]\( x = 26° \)[/tex]
Therefore, the value of x is 26°.
