Question

In the figure, BC and AD are line segments. What is the sum of x and y?

Answer 1

y = 62....interior angles of a triangle = 180
x = 54

when added, they equal (62 + 54) = 116

Answer 2

The correct option is 2.

Explanation:

Given information: BC and AD are line segments.

According to the angle sum property, the sum of interior angles of a triangle is 180°.

In triangle DOC,

`\angle C+\angle COD+\angle D=180^(\circ)`

`y+64^(\circ)+54^(\circ)=180^(\circ)`

`y+118^(\circ)=180^(\circ)`

`y=180^(\circ)-118^(\circ)`

`y=62^(\circ)`

The value of y is 62°.

If two lines intersect each other then vertical opposite angles are equal.

`\angle COD=\angle AOB=64^(\circ)`

In triangle AOB,

`\angle A+\angle AOB+\angle B=180^(\circ)`

`x+64^(\circ)+62^(\circ)=180^(\circ)`

`x+126^(\circ)=180^(\circ)`

`x=180^(\circ)-126^(\circ)`

`x=54^(\circ)`

The value of x is 54°.

The sum of x and y is

`54^(\circ)+62^(\circ)=116^(\circ)`

The sum of x and y is 116°. Therefore the correct option is 2.