Question

What is the value of w?

Answer 1

w=60°

Explanation:

triangle=180°

angle on a straight line=180°

using that,

we need to find the angle on the same line with that of "w+20°" angle, so we name it as "X"

so, 180-(w+20)=X

expand bracket by multiplying it with the "-"

so it'll be: 180-w-20=X

then rearrange to get like terms together

180-20-w=x

160-w=x

so the missing angle in the triangle is now (160-w)°

now using the angles in a triangle =180°

we add all the angles and equate it to 180, so:

w-30+w-10+160-w=180°

collect like terms again:

w+w-w-30-10+160=180

2w-w+120=180

w+120=180

move 120 to the other side and remember the sign changes, so:

w=180-120

therefore w=60°

now you can substitute w=60 into the triangle and see you'll get 180°

hope that helps

Answer 2

w = 60

Explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

w + 20 is an exterior angle of the triangle , then

w + 20 = w - 10 + w - 30

w + 20 = 2w - 40 ( subtract w from both sides )

20 = w - 40 ( add 40 to both sides )

60 = w