Question

If the m angle3 is 112 then find the value of the missing angle measure

Answer 1

Question:

Solution:

According to the diagram, we get the following equations:

Equation 1:

`m\angle1\text{ + m}\angle2=180^(\circ)`

Equation 2:

`m\angle4\text{ + m}\angle3=180^(\circ)`

the angle 3 is 112 degrees, so replacing this value into the previous equation, we get:

`m\angle4+112^(\circ)=180^(\circ)`

solving for angle 4, we get:

`m\angle4\text{ }=180^(\circ)-112^(\circ)=68^(\circ)`

now, note that

Equation 3:

`m\angle4\text{ + m}\angle1=180^(\circ)`

but the angle 4 is 68 degrees, so replacing this into the above equation, we get:

`68^(\circ)\text{ + m}\angle1=180^(\circ)`

solving for angle 1, we get :

`\text{ m}\angle1=180^(\circ)-68^(\circ)=112^(\circ)`

Finally, from equation 1, we get:

`112^(\circ)\text{ + m}\angle2=180^(\circ)`

then,

`\text{ m}\angle2=180^(\circ)-112^(\circ)=68^(\circ)`

we can conclude that the correct answer is:

`\text{ m}\angle1=112^(\circ)`

`\text{ m}\angle2=68^(\circ)`

`\text{ m}\angle3=112^(\circ)`

`m\angle4\text{ =}68^(\circ)`