To find the missing angles we are going to use two properties.
The complementary angle: that wen a line cross another line the sum of bout angles will be equal to 180 for example:
The sum of the internal angles: The sum of the internal angle of a triangle must be equal to 180 for eample:
So in the example you send me, first we calculate the complementary angle of 110 so:
[tex]\begin{gathered} 110+x=180 \\ x=70º \end{gathered}[/tex]
Now we find the missing angle of the big triangle so:
[tex]\begin{gathered} 70+70+x=180 \\ x=180-140 \\ x=40 \end{gathered}[/tex]
Now for opposite angles and alternate angles we know that the first internal angle of the small triangle is also 40º
For the same statement the oposit angle of 98º will be another internal angle of the small triangle, and we can calculate the last internal angle so:
[tex]\begin{gathered} 40+98+x=180 \\ x=42 \end{gathered}[/tex]
and finaly the missing angle will be the complementary angle of 42 so:
[tex]\begin{gathered} \text{?}+42=180 \\ \text{?}=180-42 \\ \text{?}=138º \end{gathered}[/tex]
