Question

interior and exterior triangle angles
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question
in awxy, overline{wy} is extended through point y to point z,
mangle wxy=(3x + 13)^{circ}, mangle ywx=(3x + 5)^{circ},
mangle xyz=(8x - 6)^{circ},
and
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triangles & angles hw #5
no late credit
grade: 0% complete: 50%

name angles

> vertical/adjacent/complementary angles l2

> the triangle inequality

interior and exterior triangle angles

finding angles in transversal problems (level 2)

finding angles (level 1)

finding angles (level 2)

Explanation:

Step1: Use 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.
So, \(m\angle WXY=m\angle YWX + m\angle XYZ\).
Substitute the given expressions: \(3x + 13=(3x + 5)+(8x-6)\).

Step2: Simplify the right - hand side

First, simplify \((3x + 5)+(8x-6)\):

$$
LATEXBLOCK0
$$

So the equation becomes \(3x + 13=11x-1\).

Step3: Solve for \(x\)

Subtract \(3x\) from both sides:
\(3x+13-3x=11x - 1-3x\)
\(13 = 8x-1\).
Add \(1\) to both sides: \(13 + 1=8x-1+1\)
\(14 = 8x\).
Divide both sides by \(8\): \(x=\frac{14}{8}=\frac{7}{4}=1.75\).

Answer:

\(x = 1.75\)