Question

Find the value of x in the image below

Answer 1

Hi,

115°

Explanation:

With a picture:

`\angle{DBC}=360^o -330^o=30^o\\\\\angle{\alpha}+\angle{\beta}+\angle{\gamma}+\angle{\delta}=360^o\\\\\angle{\delta}=360^o -\angle{\alpha}-\angle{\beta}-\angle{\gamma}=360^o-20^o- 65^o-30^o=245^o\\\\\angle{x}=360^o -245^o=115^o\\`

Answer 2

Explanation:

first, the angle on top of the 65° angle is also 65° (just upside down, as the "across" angles of 2 crossing lines must be identical).

second, the inner right up angle is the remainder of a full circle minus the 330° :

360 - 330 = 30°

now, we must remember that the sum of all angles in a triangle is always 180°, and the sum of all angles in a quadrilateral is always 360°.

and then we first build triangles by extending the line of the 20° angle to x all the way to the right-most line.

this has 2 angles we know : 65° and 20°.

so, the angle on the right side is

180 - 65 - 20 = 95°

and we extend the line of the 30° (remember, 360 - 330) angle to x all the way to the left-most line.

this also has 2 angles we know : 65° and 30°.

zu, the angle on the left side is

180 - 65 - 30 = 85°

now we have a quadrilateral in the middle of things :

the 2 main lines, and the 2 extended lines.

the bottom angle is the upside-down 65°.

the left angle is 85°.

the right angle is 95°.

the fourth, top angle is x (again as upside-down version of the original x angle, because of "across" angles of crossing lines are equal).

and so, we can calculate :

x = 360 - 65 - 85 - 95 = 115°