Question

4、 in a figure, m∠a = 15x + 81 and m∠c = 10x + 24. if ∠a and ∠c are supplementar find the measure of angle c.

Explanation:

Answer:

First, since ∠a and ∠c are supplementary, their measures add up to 180 degrees. So we set up the equation:
\( (15x + 81) + (10x + 24) = 180 \)
Combine like terms:
\( 25x + 105 = 180 \)
Subtract 105 from both sides:
\( 25x = 75 \)
Divide both sides by 25:
\( x = 3 \)

Now substitute \( x = 3 \) into the expression for \( m\angle c \):
\( m\angle c = 10x + 24 = 10(3) + 24 = 30 + 24 = 54 \)

So the measure of angle c is \( 54^\circ \).