Question

lines de and ab intersect at point c. what is the value of x? 12 25 38 52

Explanation:

Step1: Identify supplementary angles

Angles \( (2x + 2)^\circ \) and \( (5x + 3)^\circ \) are supplementary (they form a linear pair), so their sum is \( 180^\circ \).
\[
(2x + 2) + (5x + 3) = 180
\]

Step2: Combine like terms

Combine the \( x \)-terms and constant terms:
\[
2x + 5x + 2 + 3 = 180 \\
7x + 5 = 180
\]

Step3: Solve for \( x \)

Subtract 5 from both sides:
\[
7x = 180 - 5 \\
7x = 175
\]
Divide both sides by 7:
\[
x = \frac{175}{7} \\
x = 25
\]

Answer:

25