Question

in the figure below, suppose ( mangle3 = 43^circ ) and ( mangle4 = 78^circ ).
complete the statements below.
the sum of the interior angle measures of a triangle must be ( square^circ ).
so, ( mangle2 + mangle3 + mangle4 = square^circ ).
we are given that ( mangle3 = 43^circ ) and ( mangle4 = 78^circ ).
therefore, ( mangle3 + mangle4 = square^circ ).
and so ( mangle2 = square^circ ).
from the figure, we can see that ( mangle1 + mangle2 = square^circ ).
using the value we already found for ( mangle2 ), we find that ( mangle1 = square^circ ).
therefore, ( mangle1 ) select ( mangle3 + mangle4 ).
this result is an example of the exterior angle property of triangles.
for any triangle, the measure of an exterior angle
select

Explanation:

Step1: Recall triangle angle sum

The sum of interior angles of a triangle is \(180^\circ\). So, \(m\angle2 + m\angle3 + m\angle4 = 180^\circ\).

Step2: Calculate \(m\angle3 + m\angle4\)

Given \(m\angle3 = 43^\circ\) and \(m\angle4 = 78^\circ\), then \(m\angle3 + m\angle4 = 43^\circ + 78^\circ = 121^\circ\).

Step3: Find \(m\angle2\)

Using \(m\angle2 + 121^\circ = 180^\circ\), so \(m\angle2 = 180^\circ - 121^\circ = 59^\circ\).

Step4: Recall linear pair angle sum

\(\angle1\) and \(\angle2\) form a linear pair, so \(m\angle1 + m\angle2 = 180^\circ\).

Step5: Find \(m\angle1\)

Substitute \(m\angle2 = 59^\circ\) into \(m\angle1 + 59^\circ = 180^\circ\), we get \(m\angle1 = 180^\circ - 59^\circ = 121^\circ\).

Step6: Compare \(m\angle1\) and \(m\angle3 + m\angle4\)

Since \(m\angle1 = 121^\circ\) and \(m\angle3 + m\angle4 = 121^\circ\), so \(m\angle1 = m\angle3 + m\angle4\).

Answer:

s (filling the boxes in order):
180, 180, 121, 59, 180, 121, \(=\)