Question

I have to find what the measurements for angles using what I know from angle 10 which is 95°9.13.11.14.12.15.16.

Answer 1

The sum of linear pair of angles is 180 degrees.

So,

$\angle10+\angle9=180^{\circ}$

Substitute 95 for angle 10 in the equation to obtain the value of angle 9.

$\begin{gathered} 95^{\circ}+\angle9=180^{\circ} \\ \angle9=180^{\circ}-95^{\circ} \\ =85^{\circ} \end{gathered}$

The pair of vertically opposite angles are equal, so

$\angle9=\angle11$

and

$\angle10=\angle12$

Determine value of angle 11 and angle 12.

$\angle11=85^{\circ}$

and

$\angle12=95^{\circ}$

The pair of vertically opposite angles are equal, so

$\angle13=\angle9$$\angle16=\angle12$$\angle10=\angle14$$\angle11=\angle15$

Determine the measurement of angle 13, angle 14, angle 15 and angle 16.

$\angle13=85^{\circ}$$\angle14=95^{\circ}$$\angle15=85^{\circ}$$\angle16=95^{\circ}$

Thus, measurement of all the angles are as,

angle 9 = 85 degree

angle 10 = 95 degree

angle 11 = 85 degree

angle 12 = 95 degree

angle 13 = 85 degree

angle 14 = 95 degree

angle 15 = 85 degree

angle 16 = 95 degree