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:

$\text{ m}\angle1=112^{\circ}$

$\text{ m}\angle2=68^{\circ}$

$\text{ m}\angle3=112^{\circ}$

$m\angle4\text{ =}68^{\circ}$