Question

Please help me with number ten and twelve

Answer 1

Answer:
`93,\ 34^(\circ)`

Explanation:

Given

For figure (i) both triangles are congruent

`\therefore 8x-27=4x+33\\\Rightarrow 8x-4x=33+27\\\Rightarrow 4x=60\\\Rightarrow x=15`

`\Rightarrow PQ=8x-27\\\Rightarrow PQ=93`

For figure (ii)

Two triangles WXZ and WZY are congruent

`\therefore 9x-28=5x-8\\\Rightarrow 4x=20\\\Rightarrow x=5^(\circ)\\\Rightarrow \angle YWX=2(9x-28)\\\Rightarrow \angle YWX=2(17)\\\Rightarrow \angle YWX=34^(\circ)`