Question

The figure is not drawn to scalePQ and MN are straight lines. What is the sum of

Answer 1

Given that,

`\bar{PQ}\cong\bar{\bar{MN}}(S\text{ince both are straight lines)}`

Solving for angle x

`\angle x+86^0=180^0(s\text{um of angles on a straight line)}`

Subtract 86° from both sides

`\begin{gathered} \angle x+86^0-86^0=180^0-86^0 \\ \angle x+0=94^0 \\ \angle x=94^0 \end{gathered}`

Solving for angle y

`\angle y+30^0+86^0=180^0(s\text{um of angles on a straight line)}`
`\angle y+116^0=180^0`

Subtract 116° from both sides

`\begin{gathered} \angle y+116^0-116^0=180^0-116^0 \\ \angle y+0=64^0 \\ \angle y=64^0 \end{gathered}`

Therefore,

`\begin{gathered} m\angle x+m\angle y=\angle x+\angle y=94^0+64^0 \\ m\angle x+m\angle y=158^0 \\ \therefore m\angle x+m\angle y=158^0 \end{gathered}`

The answer is

`m\angle x+m\angle y=158^0`