Question

question #12 select all the true statements about the figure below. a x = y b x + y = 180 c y = z d x + z = 180 e y + z = 180

Explanation:

Step1: Find the value of \(x\)

Using the triangle - angle sum property (the sum of interior angles of a triangle is \(180^{\circ}\)), we have \(x + 15+43 = 180\).

$$x=180-(15 + 43)=122$$

Step2: Analyze option A

If \(x = y\), but \(y\) is the supplement of \(x\) (since \(x\) and \(y\) form a linear pair), \(y=180 - x=58
eq x\), so option A is false.

Step3: Analyze option B

If \(x + y=180\), because \(x\) and \(y\) form a linear pair (adjacent angles on a straight line), by the definition of a linear pair of angles, \(x + y = 180\), so option B is true.

Step4: Analyze option C

If \(y = z\), \(z\) is an exterior angle of the triangle. Using the exterior - angle property (an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles), \(z=15 + 43=58\), and \(y = 180 - x=58\), so \(y = z\), option C is true.

Step5: Analyze option D

If \(x+z = 180\), \(x = 122\) and \(z = 58\), \(x+z=122 + 58=180\), so option D is true.

Step6: Analyze option E

If \(y + z=180\), \(y = 58\) and \(z = 58\), \(y + z=116
eq180\), so option E is false.

Answer:

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