Question

Mr. Dinelli created this figure on his computer screen, where
←→
A
D
,
←→
E
C
, and
−−→
O
B
intersect at point O.

Angle A-O-B is y degrees, angle B-O-C is 57 degrees, and angle D-O-E is 85 degrees.

Which equation can be solved to find the value of y in this diagram?

A.
y
+
57
+
85
=
180

B.
y
+
57
+
85
=
175

C.
y
−
57
=
85

D.
y
+
57
=
85

Answer 1

To determine which equation can be solved to find the value of \( y \), we need to analyze the angles formed at point \( O \).

From the description, we know:
- \( \angle AOB = y \) degrees
- \( \angle BOC = 57 \) degrees
- \( \angle DOE = 85 \) degrees

The angles \( AOB \) and \( BOC \) are on one side of line \( OE \) (extending from points A to D) whereas \( DOE \) lies on the opposite side. Since these angles are around point \( O \), they all add up to 360 degrees.

However, more typically, angles \( AOB \) and \( BOC \) can be considered as adjacent angles when drawn, which means they typically fit around a straight line when combined with their respective adjacent angles and should sum to 180 degrees when combined linearly into straight angles.

From the configuration, we can deduce:
1. \( \angle AOB + \angle BOC + \angle DOE = 180 \)

This is particularly helpful since angles \( AOB \) and \( BOC \) will directly relate to angle \( DOE \) forming opposite angles.

Thus, we finalize:
- \( y + 57 + 85 = 180 \)

As such, the equation we seek corresponds to option **A**:

**Answer: A. \( y + 57 + 85 = 180 \)**