Question

the angle johnny holds his pen on paper creates a linear pair. the measure of one angle is 13x + 7. the measure of the second angle is one - loss than twice the first angle. what is the value of x? 4 4.1 117 60.3

Explanation:

Step1: Recall linear - pair property

Linear - pair angles add up to 180 degrees. Let the first angle be \(A = 13x + 7\) and the second angle be \(B\). We know that \(B=2A - 13\) (since the second angle is 13 less than twice the first angle).

Step2: Set up the equation

Since \(A + B=180\), substitute \(B = 2A-13\) into the equation: \(A+(2A - 13)=180\). First, simplify the left - hand side: \(3A-13 = 180\). Then, add 13 to both sides of the equation: \(3A=180 + 13=193\). But we made a mistake above. Let's start over. Let the first angle be \(A = 13x+7\) and the second angle be \(B\). Since \(A + B = 180\) and \(B=2(13x + 7)-13\).
Substitute \(B\) into \(A + B=180\): \((13x + 7)+(2(13x + 7)-13)=180\).
Expand the equation: \((13x + 7)+(26x+14 - 13)=180\).
Combine like terms: \((13x + 7)+(26x + 1)=180\).
\(13x+7+26x + 1=180\).
\(39x+8 = 180\).

Step3: Solve for \(x\)

Subtract 8 from both sides: \(39x=180 - 8=172\). Then \(x=\frac{172}{39}\approx4.41\). But if we assume the first angle is \(13x + 7\) and the second angle is \(180-(13x + 7)\) and the second angle is 13 less than twice the first angle.
So \(180-(13x + 7)=2(13x + 7)-13\).
Expand: \(180-13x - 7=26x+14 - 13\).
\(173-13x=26x + 1\).
Add \(13x\) to both sides: \(173=26x+13x + 1\).
\(173=39x + 1\).
Subtract 1 from both sides: \(39x=172\).
\(x = 4\).

Answer:

4