Question

find the measure of each marked angle. the larger angle measures 109°. the smaller angle measures □°.

Explanation:

Step1: Set up an equation

Since the two marked - angles are supplementary (they form a straight - line and their sum is 180°), we have the equation \((13x + 5)+(8x+7)=180\).

Step2: Combine like terms

Combining the \(x\) terms and the constant terms, we get \(13x+8x + 5 + 7=180\), which simplifies to \(21x+12 = 180\).

Step3: Isolate the variable term

Subtract 12 from both sides of the equation: \(21x=180 - 12\), so \(21x=168\).

Step4: Solve for \(x\)

Divide both sides by 21: \(x=\frac{168}{21}=8\).

Step5: Find the measure of each angle

For the first angle \((13x + 5)\), substitute \(x = 8\): \(13\times8+5=104 + 5=109^{\circ}\).
For the second angle \((8x + 7)\), substitute \(x = 8\): \(8\times8+7=64 + 7=71^{\circ}\).

Answer:

The smaller angle measures \(71^{\circ}\), the larger angle measures \(109^{\circ}\).