Question

calculate the value of x.
x = 84
x = 96
x = 32
none of these

Explanation:

Step1: Find the value of \( y \)

Use the triangle - angle sum formula (\( a + b + c=180^{\circ} \) for a triangle with angles \( a,b,c \)).
\( y + 58^{\circ}+26^{\circ}=180^{\circ} \)
\( y=180^{\circ}-(58^{\circ} + 26^{\circ}) \)
\( y = 96^{\circ} \)

Step2: Find the value of \( x \)

Use the linear - pair formula (\( x + y=180^{\circ} \) since \( x \) and \( y \) form a linear pair).
\( x=180^{\circ}-y \)
Substitute \( y = 96^{\circ} \) into the formula:
\( x=180^{\circ}-96^{\circ} \)
\( x = 84^{\circ} \)

Answer:

\( x = 84 \)