Question

find the measure of each angle in the diagram write and solve an equation in the diagram angle 2 is right angle

Answer 1

• m∠2 = 90°

,

• m∠3 = 73°

,

• m∠4 = 17°

,

• m∠5 = 90°

,

• m∠6 = 73°

Step-by-step explanation:

Angle 2 is a right angle, therefore:

• m∠2 = 90°

Given that m∠1 = 17°:

`m\angle1+m\angle2+m\angle3=180\degree\text{ (Angle on a straight line)}`

Substitute the given values:

`\begin{gathered} 17\degree+90\degree+m\angle3=180\degree \\ 107\degree+m\angle3=180\degree \\ m\angle3=180\degree-107\degree \\ m\angle3=73\degree \end{gathered}`

• m∠3 = 73°

Angles 1 and 4 are vertically opposite angles, therefore:

`\begin{gathered} m\angle4=m\angle1 \\ m\angle4=17\degree \end{gathered}`

Angles 2 and 5 are vertically opposite angles, therefore:

`\begin{gathered} m\angle5=m\angle2 \\ m\angle5=90\degree \end{gathered}`

Angles 3 and 6 are vertically opposite angles, therefore:

`\begin{gathered} m\angle6=m\angle3 \\ m\angle6=73\degree \end{gathered}`