- In order to calculate the value of x in the given figure, you take into account that the angle A to the left of the angle 130° is:
180° - 130° = 50°
Next, you also take into account that the right triangle is isosceles, that is, two sides are equal. This also means tha the angle B of the right triangle is 50°
Finally, you use the fact that the sum of all angles inside a triagle must be 180°. Thus, you have:
50° + 50° + x = 180° you solve for x
100° + x = 180°
x = 180° - |00°
x = 80°
Hence, the value of angle x is x = 80°
- For the second figure you have that the left triangle is an equilateral triangle. Furthermore, the bigger traingle ABC is a rectangle triangle. Because of that angle B has to be 90°, but you already have angle there of 45°; hence, the angle to the left of the angle 45° and inside the equilateral angñe has to be also 45° (45°+45°=90°). Thus, y = 45°
The rest of the angles inside the equilateral triangle are also of 45°
Next, you consider that the sum of angles of the triangle ABC must be 180°. Then, for angle x, you have:
45° + 90° + x = 180°
135° + x = |80°
x = 180° - |35°
x = 45°
Hence, x and y angles are x=45°, y=45°