Question

in $\triangle mno$, $\overline{mo}$ is extended through point o to point p, $m\angle mno = (2x - 3)\degree$, $m\angle omn = (3x + 14)\degree$, and $m\angle nop = (8x - 19)\degree$. what is the value of $x$?
answer attempt 1 out of 2
$x = \square$ submit answer

Explanation:

Step1: Apply the exterior - angle theorem

The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
In \(\triangle MNO\), \(\angle NOP\) is an exterior angle, and \(\angle MNO\) and \(\angle OMN\) are the two non - adjacent interior angles. So, \(m\angle NOP=m\angle MNO + m\angle OMN\).
Substitute the given angle measures: \((8x - 19)=(2x - 3)+(3x + 14)\).

Step2: Simplify the right - hand side of the equation

Simplify \((2x - 3)+(3x + 14)\):

$$
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So the equation becomes \(8x-19 = 5x + 11\).

Step3: Solve for \(x\)

Subtract \(5x\) from both sides of the equation:
\(8x-5x-19=5x - 5x+11\), which simplifies to \(3x-19 = 11\).
Add \(19\) to both sides: \(3x-19 + 19=11 + 19\), so \(3x=30\).
Divide both sides by \(3\): \(x=\frac{30}{3}=10\).

Answer:

\(x = 10\)