Question

in the figure below, suppose ( mangle 3 = 118^circ ) and ( mangle 4 = 32^circ ).
complete the statements below.
the sum of the interior angle measures of a triangle must be (square^circ).
so, ( mangle 2 + mangle 3 + mangle 4 = square^circ ).
we are given that ( mangle 3 = 118^circ ) and ( mangle 4 = 32^circ ).
therefore, ( mangle 3 + mangle 4 = square^circ ).
and so ( mangle 2 = square^circ ).
from the figure, we can see that ( mangle 1 + mangle 2 = square^circ ).
using the value we already found for ( mangle 2 ), we find that ( mangle 1 = square^circ ).

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles of a triangle is \(180^\circ\). So, \(m\angle 2 + m\angle 3 + m\angle 4 = 180^\circ\).

Step2: Calculate \(m\angle 3 + m\angle 4\)

Given \(m\angle 3 = 118^\circ\) and \(m\angle 4 = 32^\circ\), add them: \(118 + 32 = 150^\circ\).

Step3: Find \(m\angle 2\)

Using \(m\angle 2 + 150 = 180\), solve for \(m\angle 2\): \(m\angle 2 = 180 - 150 = 30^\circ\).

Step4: Recall linear pair sum

\(\angle 1\) and \(\angle 2\) form a linear pair, so \(m\angle 1 + m\angle 2 = 180^\circ\).

Step5: Find \(m\angle 1\)

Substitute \(m\angle 2 = 30^\circ\) into \(m\angle 1 + 30 = 180\), solve: \(m\angle 1 = 180 - 30 = 150^\circ\).

Answer:

s (filling the blanks):

1. The sum of the interior angle measures of a triangle must be \(\boldsymbol{180}\)°.
2. So, \(m\angle 2 + m\angle 3 + m\angle 4 = \boldsymbol{180}\)°.
3. Therefore, \(m\angle 3 + m\angle 4 = \boldsymbol{150}\)°.
4. And so \(m\angle 2 = \boldsymbol{30}\)°.
5. From the figure, we can see that \(m\angle 1 + m\angle 2 = \boldsymbol{180}\)°.
6. Using the value we already found for \(m\angle 2\), we find that \(m\angle 1 = \boldsymbol{150}\)°.