MATH SOLVE

4 months ago

Q:
# Which statements about the diagram are true? Select three options.x = 63y = 47z = 117x + y = 180x + z = 180

Accepted Solution

A:

Answer:x = 63z = 117x + z = 180Step-by-step explanation:x is a "corresponding" angle for the one marked 63°. Here, corresponding angles are congruent, so x = 63°.__x and z are "same-side interior angles," so are supplementary. Their sum is 180°. x + z = 180°.__Because x and z are supplementary and z and 63° are supplementary, you know that ... z = 180° -63° z = 117°_____Comments on the other answer choicesThe value of y can be computed using the fact that the sum of angles interior to the triangle is 180°. The unmarked triangle interior angle is a vertical angle to the one labeled 63°, so it is 63°. Then the value of y is ... y° = 180° -47° -63° = 70° . . . . . . . not 47°__We already know that 63° + y + 47° = 180° and x = 63°. That means ... x + y + 47° = 180°so it cannot be true that x+y = 180.