Question

line ac intersects line bd at point o.
if ( mangle boc=(3x + 1)^{circ} ) and ( mangle cod=(11x - 3)^{circ} ), what is ( mangle cod )?
13°
40°
69°
140°

Explanation:

Step1: Use the property of adjacent angles on a straight line

Since \(\angle BOC\) and \(\angle COD\) are adjacent angles on a straight line (they form a linear - pair), \(m\angle BOC+m\angle COD = 180^{\circ}\).
Substitute \(m\angle BOC=(3x + 1)^{\circ}\) and \(m\angle COD=(11x-3)^{\circ}\) into the equation: \((3x + 1)+(11x-3)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+11x+1 - 3=180\), which gives \(14x-2 = 180\).
Add \(2\) to both sides of the equation: \(14x-2 + 2=180+2\), so \(14x=182\).

Step3: Solve for \(x\)

Divide both sides by \(14\): \(x=\frac{182}{14}=13\).

Step4: Find \(m\angle COD\)

Substitute \(x = 13\) into the expression for \(m\angle COD\): \(m\angle COD=(11x-3)^{\circ}\).
\(m\angle COD=(11\times13 - 3)^{\circ}=(143-3)^{\circ}=140^{\circ}\).

Answer:

\(140^{\circ}\)