Question

question 1: (gr.1.1)
lines \\( \overline{z h} \\), \\( \overline{c b} \\), \\( \overline{n k} \\), and \\( \overline{g m} \\) are shown.
\\( \overline{z h} \\| \overline{c b} \\)
\\( \angle z j l=40^{\circ}, \angle g l j=64^{\circ}, \angle g f z=(3 x+10)^{\circ} \\), and \\( \angle z f v=(5 x-6)^{\circ} \\)
complete the table.

Explanation:

Step1: Find the value of \(x\)

Since \(\angle GFZ\) and \(\angle ZFV\) are supplementary (they form a linear pair), we have \((3x + 10)+(5x - 6)=180\).
Simplify the left - hand side: \(3x+10 + 5x-6=8x + 4\).
So, \(8x+4 = 180\).
Subtract 4 from both sides: \(8x=180 - 4=176\).
Divide both sides by 8: \(x=\frac{176}{8}=22\).

Step2: Find the value of \(\angle GFZ\)

Substitute \(x = 22\) into the expression for \(\angle GFZ\): \(\angle GFZ=(3x + 10)^{\circ}\).
\(\angle GFZ=(3\times22+10)^{\circ}=(66 + 10)^{\circ}=76^{\circ}\).

Step3: Find the value of \(\angle ZFV\)

Substitute \(x = 22\) into the expression for \(\angle ZFV\): \(\angle ZFV=(5x - 6)^{\circ}\).
\(\angle ZFV=(5\times22-6)^{\circ}=(110 - 6)^{\circ}=104^{\circ}\).

Answer:

1. \(22\)
2. \(76^{\circ}\)
3. \(104^{\circ}\)