Question

Please help i need the answers for a test and how to work em out for the future

Answer 1

Given: The angles as shown in the image

To Determine: The measure of angle DEF

Solution

It can be observed that

`\begin{gathered} 105^0+6x+3=27x+3 \\ 105=27x-6x+3-3 \\ 105=21x \\ x=(105)/(21) \\ x=5 \end{gathered}`

Question 12

Given:

`\begin{gathered} m\angle UIJ=x+43 \\ m\angle HIJ=66 \\ m\angle HIU=x+37 \end{gathered}`

To Determine: The measure of angle HIU

Solution:

It can be observed that

`m\angle UIJ+m\angle HIU=m\angle HIJ`
`\begin{gathered} x+43+x+37=66^0 \\ Collect-like-terms \\ x+x+43^0+37^0=66^0 \\ 2x+80^0=66^0 \\ 2x=66^0-80^0 \\ 2x=-14^0 \\ x=-(14^0)/(2) \\ x=-7^0 \end{gathered}`

Therefore, the measure of angle HIU would be

`\begin{gathered} m\angle HIU=x+37^0 \\ m\angle HIU=-7+37^0 \\ m\angle HIU=30^0 \end{gathered}`

Hence, the measure of angle HIU is 30⁰