Question

A carpenter's square is used on the circular part of a blueprint. SQ = UQ.What is the measure of SQ?60°90°SU45°180°180°

Answer 1

Step 1: Observe the given figure state the obvious angles

`\text{SQU}=90^0(\text{angle in a semicircle)}`
`SQ\cong QU(given)`
`\begin{gathered} \text{If SQ}\cong QU,\text{ then }\Delta SQU\text{ is an isosceles triangle} \\ \text{Hence, the base angles are equal} \end{gathered}`
`i\mathrm{}e\text{. QSU}=\text{QUS}`
`\begin{gathered} \text{QSU}+\text{QUS}=90^0(\text{Complimentary angles)} \\ 2\text{QUS}=90^0 \\ \text{QUS}=(90^0)/(2) \end{gathered}`
`\text{QUS}=45^0`

Hence, arc QS=45°