Question

Use the diagram below. What is the value of z?

(Picture included) it would mean sm if anyone could help

Answer 1

`z = 29°`

Explanation:

According to the triangle angle sum theorem, the sum of the interior angles of a triangle is 180°. So for
`\triangle{ABD},` the sum of its interior angles is

`43 + 59 + x = 180`

`\Rightarrow x = 78°`

But
`\angle{x}` is supplementary with
`\angle{y}` so that

`x + y = 180 \Rightarrow y = 180 - 78 = 102°`

Now that we know the value of y, we apply the triangle angle sum theorem to
`\triangle{BDC}` and we get

`49 + y + z = 180 \Rightarrow 49 + 102 + z = 180`

Solving for z, we finally get

`z = 29°`