The question pertains to the angle property of a triangle.
The angle property of a triangle states that:
" The sum of all interior angles in a triangle is always equal to 180 degrees "
We will apply the angle property of the triangle and find the required numbered ( 1 ) interior angle in each figure.
The first figure delineates a triangular shape of a mountain. Where two of the interior angles made between the slant heights of the mountain and the ground are given as follows:
[tex]61\text{ degrees , 59 degrees }[/tex]We will go ahead and express the angle property law of triangles in a mathematical form:
[tex]\angle\textcolor{#FF7968}{1}\text{ + 61 + 59 = 180}[/tex]We will go ahead and manipulate the above equation and determine the angle ( < 1 ) as follows:
[tex]\begin{gathered} \angle1\text{ + 120 = 180 } \\ \angle1\text{ = 180 - 120} \\ \textcolor{#FF7968}{\angle1=}\text{\textcolor{#FF7968}{ 60 degrees}} \end{gathered}[/tex]Hence, the required numbered interior angle for mountain figure is:
[tex]\textcolor{#FF7968}{60}\text{\textcolor{#FF7968}{ degrees}}[/tex]================================================================================
The next figure models the triangular shape of the roof of a house. The interior angle formed between the slant heights of the roof and the horizontal base of the roof , and the vertex of the triangle is given as follows:
[tex]125\text{ degrees , 35 degrees}[/tex]We will again apply the interior angle law for triangles which states:
[tex]\angle1\text{ + 125 + 35 = 180}[/tex]We will go ahead and manipulate the above equation and determine the angle ( < 1 ) as follows:
[tex]\begin{gathered} \angle1\text{ + 160 = 180} \\ \angle1\text{ = 180 - 160} \\ \textcolor{#FF7968}{\angle1}\text{\textcolor{#FF7968}{ = 20 degrees}} \end{gathered}[/tex]Hence, the required numbered interior angle for house roof figure is:
[tex]\textcolor{#FF7968}{20}\text{\textcolor{#FF7968}{ degrees}}[/tex]