Question

1. select all the equations that represent a true relationship between the angles in the diagram shown.

a. ( x = 25 )
b. ( w = 90 )
c. ( y = 65 )
d. ( 90 + w + x = 180 )
e. ( w + x + y = 90 )

Explanation:

Step1: Identify vertical angle for $x$

Vertical angles are equal, so $x = 25^\circ$.

Step2: Identify right angle for $w$

The box marks a right angle, so $w = 90^\circ$.

Step3: Calculate $y$ using straight angle

Straight angle sums to $180^\circ$, so $y = 180^\circ - 90^\circ - 25^\circ = 65^\circ$.

Step4: Verify option D

Sum: $90 + w + x = 90 + 90 + 25 = 205
eq 180$, so false.

Step5: Verify option E

Sum: $w + x + y = 90 + 25 + 65 = 180
eq 90$, so false.

Answer:

A. $x = 25$
B. $w = 90$
C. $y = 65$