Question

geometry w/data analysis (1 cr): section 3 (lms) topic 2: assessment form a (lms graded) a triangle is shown. which of the following statements are true? select all that apply. a. x = y b. x + y = 180 c. y = z d. x + z = 180

Explanation:

Step1: Recall linear - pair property

Angles \(x\) and \(y\) form a linear pair. By the linear - pair postulate, the sum of the measures of two angles in a linear pair is \(180^{\circ}\). So \(x + y=180\).

Step2: Recall vertical - angle property

Angles \(y\) and \(z\) are vertical angles. By the vertical - angles theorem, vertical angles are congruent. So \(y = z\).

Step3: Analyze other relationships

Since \(x + y = 180\) and \(y=z\), then \(x + z=180\) (by substitution). And \(x\) and \(y\) are not equal in general (except when they are both \(90^{\circ}\), which is not the case here as we can calculate the third angle of the triangle as \(180-(82 + 54)=44^{\circ}\) and use angle - relationships to find \(x,y,z\)).

Answer:

B. \(x + y = 180\)
C. \(y = z\)
D. \(x + z = 180\)