Question

129° 1 95° 47° 5 7 121° 2 6
47
38
133
129

Explanation:

Step1: Use linear - pair property

Since the angle adjacent to the $129^{\circ}$ angle forms a linear - pair, its measure is $180 - 129=51^{\circ}$. And the angle adjacent to the $121^{\circ}$ angle forms a linear - pair, its measure is $180 - 121 = 59^{\circ}$.

Step2: Use angle - sum property of a triangle

In the right - hand triangle, we know one angle is $47^{\circ}$ and another (from the linear - pair calculation) is $59^{\circ}$. Let the third angle be $x$. By the angle - sum property of a triangle ($a + b + c=180^{\circ}$), we have $x+47 + 59=180$. So $x = 180-(47 + 59)=74^{\circ}$.

Step3: Use vertical - angle property

The angle vertical to the $95^{\circ}$ angle has a measure of $95^{\circ}$. In the left - hand triangle, we know one angle is $51^{\circ}$ and another (vertical to $95^{\circ}$) is $95^{\circ}$. Let the third angle be $y$. By the angle - sum property of a triangle, $y+51 + 95=180$. So $y=180-(51 + 95)=34^{\circ}$.

Step4: Analyze the given options

We need to find an angle measure among the options. Since the angle adjacent to the $129^{\circ}$ angle is $51^{\circ}$, the angle adjacent to the $121^{\circ}$ angle is $59^{\circ}$, the non - given angles in the triangles are $74^{\circ}$ and $34^{\circ}$, and the vertical angles are $95^{\circ}$ and the given $47^{\circ}$ angle. The only angle among the options that matches an angle in the figure is $47^{\circ}$.

Answer:

$47$