Question

The figure is not drawn to scale. PQ and SR are straight lines. FIND

Answer 1

From the given diagram,

`\begin{gathered} \angle UVQ=72^0 \\ \angle TVS=30^0 \end{gathered}`

Where line PQ and SR are straight lines

And

`m\angle QVT+m\angle TVS=m\angle QVS=90^0\text{ (complimentary angles)}`

Substitute the value of m∠TVS into the formula above

`\begin{gathered} m\angle QVT+m\angle TVS=90^0 \\ m\angle QVT+30^0=90^0 \\ \text{Collect like terms} \\ m\angle QVT=90^0-30^0=60^0 \\ m\angle QVT=60^0 \end{gathered}`

To find m∠UVT, the formula is

`m\angle UVT=m\angle UVQ+m\angle QVT`

Where

`\begin{gathered} m\angle UVQ=72^0 \\ m\angle QVT=60^0 \end{gathered}`

Substitute the values into the formula below

`\begin{gathered} m\angle UVT=m\angle UVQ+m\angle QVT \\ m\angle UVT=72^0+60^0=132^0 \\ m\angle UVT=132^0 \end{gathered}`

Hence, m∠UVT is 132°