Answer:
1. 36
2. 70°
Explanation:
Let's use process of elimination here, starting from the smallest until we reach a sweet number:
18 is not divisible by 4.
24 is not divisible by 9.
36 is divisible by 6 (6 × 6), 4 (4 × 9), and 9 (9 × 4).
We're going to have to remember some things here:
Remember that intersecting lines produce two sets of equal angles (Vertical Angles) and that the angles across from each other (Vertical Angles) are always congruent.
Triangle's angles always add up to 180°
Inside the triangle, we have a 65° angle and the value of the other two angles are currently unknown. We can see that one of the angles inside the triangle form a Vertical Angle with a 45° angle, which means it must be 45° itself. Now we have two angles in the triangle, 65° and 45°. Remember, angles inside a triangle always add up to 180°. 180 - 65 - 45 = 70. So the remaining angle in the triangle must be 70°. We notice this angle forms Vertical angles with x, therefore x must have a measurment of 70°.