Question

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what is the measure of the larger angle in degrees?
enter your answer as a decimal, if necessary, like this: 42.5

Explanation:

Step1: Use the property of supplementary angles

Since the two angles \((2.4x)^{\circ}\) and \((9.6x)^{\circ}\) are supplementary (they form a linear - pair), their sum is \(180^{\circ}\). So, \(2.4x + 9.6x=180\).

Step2: Solve the equation for \(x\)

Combine like terms: \((2.4 + 9.6)x=180\), which gives \(12x = 180\). Then, divide both sides by \(12\): \(x=\frac{180}{12}=15\).

Step3: Find the measure of the larger angle

The larger angle is \((9.6x)^{\circ}\). Substitute \(x = 15\) into \(9.6x\): \(9.6\times15=(10 - 0.4)\times15=10\times15-0.4\times15=150 - 6=144\).

Answer:

\(144\)