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solve for a. 25° 55° a 30° a = ?°

Question

solve for a.
25°
55° a 30°
a = ?°

Explanation:

Step1: Recall triangle angle sum

Triangle angles sum to $180^\circ$. Let the third angle (adjacent to $a$) be $x$. So $25^\circ + 30^\circ + x = 180^\circ$.

Step2: Calculate $x$

$x = 180^\circ - 25^\circ - 30^\circ = 125^\circ$.

Step3: Use linear pair

$a$ and $x$ (with $55^\circ$) form a linear pair? Wait, no: the $55^\circ$ and $a$ and the angle inside the triangle (let's correct: the angle adjacent to $55^\circ$ and $a$ is supplementary to $55^\circ$, but actually, the exterior angle? Wait, better: the angle adjacent to $55^\circ$ is $180^\circ - 55^\circ = 125^\circ$? No, wait the triangle has angles $25^\circ$, $30^\circ$, and the third angle. Wait, no, the $55^\circ$ is an exterior angle? Wait, no, the diagram: the left side has a $55^\circ$ angle between the side and the extension, then angle $a$ is between the two sides of the triangle, and the right angle is $30^\circ$, top angle $25^\circ$. Wait, actually, the angle adjacent to $55^\circ$ (let's call it $b$) and $a$ are supplementary? No, wait, the sum of angles in a triangle: $25^\circ + 30^\circ + (180^\circ - a) = 180^\circ$? No, that's wrong. Wait, the angle at the bottom left of the triangle (between the side and the extension) is $55^\circ$, so the interior angle there is $180^\circ - 55^\circ = 125^\circ$? No, no, the triangle's angles: the three angles are $25^\circ$, $30^\circ$, and the angle opposite to... Wait, no, the correct approach: the angle adjacent to $a$ (let's call it $c$) and $55^\circ$ are supplementary? No, the sum of angles in the triangle: $25^\circ + 30^\circ + c = 180^\circ$, so $c = 125^\circ$. Then, $c$ and $a$ and $55^\circ$? No, $c + a + 55^\circ = 180^\circ$? No, that's a straight line? Wait, no, the $55^\circ$, $a$, and $c$ are on a straight line? Wait, the diagram: the left side has a $55^\circ$ angle between the side of the triangle and the horizontal line, then angle $a$ is between the two sides of the triangle (the left side and the right side), and the right side has a $30^\circ$ angle. Wait, I think I messed up. Let's start over.

The triangle has angles: top angle $25^\circ$, right angle $30^\circ$, and the bottom left angle (let's call it $d$). Then, the angle adjacent to $55^\circ$ is $d$, so $d + 55^\circ = 180^\circ$ (linear pair), so $d = 125^\circ$. But in the triangle, $25^\circ + 30^\circ + d = 180^\circ$? No, $25 + 30 + d = 180$ would mean $d = 125$, which matches. Then, angle $a$: the sum of angles around the point? No, angle $a$ is between the two sides of the triangle, so the three angles of the triangle are $25^\circ$, $30^\circ$, and $a$? No, that can't be. Wait, no, the diagram: the triangle has vertices: top, right (30°), and the bottom vertex where angle $a$ is. The left side of the triangle is extended, forming a $55^\circ$ angle with the extension. So the interior angle at the bottom left is $180^\circ - 55^\circ = 125^\circ$? No, that's not right. Wait, the correct formula: the exterior angle (55°) is equal to the sum of the two non-adjacent interior angles. Wait, the exterior angle theorem: the exterior angle (55°) is equal to the sum of the two remote interior angles. Wait, no, the remote interior angles would be $25^\circ$ and $30^\circ$? No, 25 + 30 = 55? No, 25 + 30 = 55, which matches the exterior angle. Oh! So the exterior angle (55°) is equal to the sum of the two non-adjacent interior angles (25° and 30°), which is 55°, so that checks out. Then, angle $a$ is adjacent to the exterior angle? Wait, no, angle $a$ is the angle we need to find, which is the third angle? Wait, no, the triangle has angles:…

Answer:

100