Question

find the missing information to fill in the blanks. diagrams are not drawn to scale. do numbers 6 & 8. don’t take forever when answering both of those questions. all i care about is the steps and the answer.

Answer 1

6)

`\begin{gathered} \angle MOL=2\angle MKL\text{ (angle at centre is twice angle at circumference)} \\ 146=2(37x-1) \\ 146=74x-2 \\ 146+2=74x \\ 148=74x \\ x=(148)/(74) \\ x=2 \end{gathered}`
`\begin{gathered} To\text{ get m}\angle MKL,\text{ we have:} \\ \angle MKL=37x-1 \\ \angle MKL=37(2)-1 \\ \angle MKL=74-1 \\ \angle MKL=73^0 \end{gathered}`

Hence, the value of x=2, and the measure of angle MKL is 73 degrees

8)

`\begin{gathered} m\angle BDC=90^0(angle\text{ in a semi- circle)} \\ m\angle BAC=90^0(angle\text{ in a semi-circle)} \\ 3y+11+y+7+90=180^0(sum\text{ of interior angles in a triangle)} \\ 4y+108=180 \\ 4y=72 \\ y=(72)/(4) \\ y=18^0 \end{gathered}`
`\begin{gathered} 5x+3x+10+90=180^0(sum\text{ of interior angles in a triangle)} \\ 8x+100=180 \\ 8x=180-100 \\ 8x=80 \\ x=(80)/(8) \\ x=10^0 \end{gathered}`

Hence,

`\begin{gathered} i)\text{ m}\angle BDC=90^0 \\ ii)\text{ m}\angle DCB=5x=5*10=50^0 \\ iii)\text{ m}\angle DBC=3x+10=3(10)+10=30+10=40^0 \\ iv)\text{ m}\angle BCA=3y+11=3(18)+11=54+11=65^0 \end{gathered}`