Question

find the measure of the angle indicated in bold. 25) 26) 27) 28)

Explanation:

Step1: Analyze problem 25

The two angles \(x + 96\) are supplementary (sum to 180°). So the equation is \(2(x + 96)=180\), which simplifies to \(2x+192 = 180\). Subtracting 192 from both sides gives \(2x=180 - 192=-12\), and then \(x=-6\). But this is incorrect as angles cannot have negative - measures in this context. The correct approach is that the two angles are vertical - angles (equal), not supplementary. So \(x + 96+x + 96\) is wrong. Since they are vertical angles, they are equal.

Step2: Analyze problem 26

The two angles \(20x + 5\) and \(24x-1\) are supplementary. Set up the equation \((20x + 5)+(24x-1)=180\). Combine like - terms: \(20x+24x+5 - 1=180\), which gives \(44x + 4=180\). Subtract 4 from both sides: \(44x=180 - 4 = 176\). Then \(x=\frac{176}{44}=4\).

Step3: Analyze problem 27

The two angles \(6x\) and \(5x + 10\) are supplementary. Set up the equation \(6x+5x + 10=180\). Combine like - terms: \(11x+10 = 180\). Subtract 10 from both sides: \(11x=180 - 10=170\). Then \(x=\frac{170}{11}\).

Step4: Analyze problem 28

The two angles \(x + 109\) and \(x + 89\) are supplementary. Set up the equation \((x + 109)+(x + 89)=180\). Combine like - terms: \(2x+198 = 180\). Subtract 198 from both sides: \(2x=180 - 198=-18\). Then \(x=-9\). But angles in this context should be non - negative, and there may be an error in the setup. If they are vertical angles, we need to re - evaluate. Assuming they are supplementary, \(2x=-18\) and \(x=-9\) is wrong. If they are vertical angles, \(x + 109=x + 89\) is a contradiction. Let's assume they are supplementary correctly.

Answer:

Problem 25: Error in initial setup.
Problem 26: \(x = 4\)
Problem 27: \(x=\frac{170}{11}\)
Problem 28: Error in setup or problem statement.