Question

solve for a. a = ?°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°. Let's first find the third - interior angle of the triangle with angles 25° and 30°. Let this angle be x. So, $x+25^{\circ}+30^{\circ}=180^{\circ}$.

Step2: Solve for x

$x = 180^{\circ}-(25^{\circ}+30^{\circ})=125^{\circ}$.

Step3: Use the linear - pair property

The angle x and the angle adjacent to 55° and a form a linear pair. A linear pair of angles sums to 180°. Let the angle adjacent to 55° and a be y. So, $y + 55^{\circ}+a=180^{\circ}$. Also, since x and y are vertical angles, x = y = 125°.

Step4: Solve for a

Substitute y = 125° into $y + 55^{\circ}+a=180^{\circ}$. We get $125^{\circ}+55^{\circ}+a=180^{\circ}$, then $a=180^{\circ}-(125^{\circ}+55^{\circ}) = 0^{\circ}$. But this is wrong. Let's use the exterior - angle property.
The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. The exterior angle a is equal to the sum of the two non - adjacent interior angles of the triangle, which are 25° and 30°.
So, $a=25^{\circ}+30^{\circ}$.

Answer:

$55^{\circ}$