Question

find the error kaila solved the problem, as shown. is her solution correct? if it is, explain your reasoning. if not, explain kailas mistake and correct the work. if ( mangle f = (6x - 9)^circ ) and ( mangle g = (2x + 13)^circ ), find the value of ( x ) such that ( angle f ) and ( angle g ) are supplementary. ( (6x - 9)^circ + (2x + 13)^circ = 90^circ ) ( 8x^circ - 4^circ = 90^circ ) ( 8x^circ = 86^circ ) ( x = 10.75 )

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles sum to \(180^{\circ}\), not \(90^{\circ}\). Kaila used the wrong sum.

Step2: Set up the correct equation

\((6x - 9)+(2x + 13)=180\)

Step3: Simplify the left - hand side

\(6x-9 + 2x+13=8x + 4\)
So the equation becomes \(8x+4 = 180\)

Step4: Solve for \(x\)

Subtract \(4\) from both sides: \(8x=180 - 4=176\)
Divide both sides by \(8\): \(x=\frac{176}{8}=22\)

Answer:

Kaila's solution is incorrect. She used the sum of complementary angles (\(90^{\circ}\)) instead of supplementary angles (\(180^{\circ}\)). The correct value of \(x\) is \(22\).