A leftward ray originating at x has points y and z marked on it. A triangle x w y has angle x measuring 3 y degrees and angle w measuring left parenthesis 4 y minus 4 right

Question

Use the Triangle Angle Sum Theorem to find the measure of angle at point W
for the triangle in the diagram.

(1 point)
Responses

128°
128 degrees

26°
26 degrees

24°
24 degrees

28°
28 degrees

Answer 1

To find the measure of angle \( w \) in triangle \( xwy \), we can apply the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is \( 180^\circ \).

Given:

• Angle \( x = 3y \)
• Angle \( w = 4y - 4 \)
• Angle \( y \) (we'll denote this as simply \( y \))

According to the Triangle Angle Sum Theorem: \[ 3y + (4y - 4) + y = 180 \]

Now, combine the terms: \[ 3y + 4y - 4 + y = 180 \] \[ 8y - 4 = 180 \]

Next, add \( 4 \) to both sides: \[ 8y = 184 \]

Now, divide by \( 8 \): \[ y = 23 \]

Now we can find the measure of angle \( w \): \[ w = 4y - 4 \] Substituting \( y = 23 \): \[ w = 4(23) - 4 = 92 - 4 = 88 \]

We still need to check that the angles sum to \( 180^\circ \):

• Angle \( x = 3y = 3(23) = 69^\circ \)
• Angle \( y = 23^\circ \)
• Angle \( w = 88^\circ \)

Now verify the angle sum: \[ 69 + 23 + 88 = 180^\circ \]

Thus, the measure of angle \( w \) is \( 88^\circ \).

It seems that there might be no options matching. However, based on the algebra, if we only consider possible given angle measures, then the answer provided doesn’t conform to \( 88^\circ \). Please verify if the question has accurate values or if other angles need re-evaluation.