Math  /  Geometry

QuestionGiven the diagram at the right, prove that mw=my+mzm \angle w=m \angle \boldsymbol{y}+m \angle \boldsymbol{z}.

Studdy Solution

STEP 1

1. The diagram consists of a straight line and a ray extending from it.
2. Angles y y and z z are adjacent angles formed by the ray.
3. Angle w w is the larger angle formed by the straight line and the ray.

STEP 2

1. Identify the relationship between the angles.
2. Use the Angle Addition Postulate to prove the relationship.

STEP 3

Identify the relationship between the angles. Since y y and z z are adjacent angles formed by the ray on the straight line, they together make up the angle w w .

STEP 4

Apply the Angle Addition Postulate, which states that if a point lies in the interior of an angle, then the measure of the angle is the sum of the measures of the two adjacent angles formed. In this case, the ray divides angle w w into angles y y and z z .

STEP 5

According to the Angle Addition Postulate, we have:
mw=my+mz m \angle w = m \angle y + m \angle z
This proves that the measure of angle w w is indeed the sum of the measures of angles y y and z z .
The proof is complete, and we have shown that:
mw=my+mz m \angle w = m \angle y + m \angle z

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