Question

a line intersects two parallel lines, forming four acute angles and four obtuse angles. the measure of one of the acute angles is (9x - 650)°. the sum of the measures of one of the acute angles and three of the obtuse angles is (-18x + w)°. what is the value of w? enter your numerical answer. enter your answer... enter your answer as a number, fraction, or decimal. question 19 of 22 math - module2

Explanation:

Step1: Recall angle - relationship property

When a line intersects two parallel lines, corresponding angles are equal, and the sum of an acute - angle and an obtuse - angle is 180°. Since the sum of the measures of one of the acute angles and three of the obtuse angles is \((-18x + w)^{\circ}\), and we know that an acute angle \((9x-650)^{\circ}\) and the related obtuse - angle sum to 180°.
The sum of one acute and three obtuse angles can be written in terms of the acute - angle measure. Let the acute - angle measure be \(A=(9x - 650)^{\circ}\), and the obtuse - angle measure be \(O = 180-(9x - 650)=(930 - 9x)^{\circ}\).
The sum of one acute and three obtuse angles is \(A + 3O=(9x-650)+3(930 - 9x)\).

Step2: Expand and simplify the expression

\[

$$\begin{align*} (9x-650)+3(930 - 9x)&=9x-650 + 2790-27x\\ &=(9x-27x)+(-650 + 2790)\\ &=-18x+2140 \end{align*}$$

\]
Since \(-18x + w=-18x+2140\), by comparing the two expressions, we can see that \(w = 2140\).

Answer:

2140