Find the values of x and y. Justify your answers by stating the postulates, theorems, or definitions used for each step.

Step-by-step explanation:

10) From the diagram you can see that the diagram at the right hand side is am isosceles triangle. An isosceles triangle is triangle that has its two base angles equal. Hence

x = 75°

Reason: Base angle of an isosceles triangle are equal.

To get y:

First we need to find the third angle of the isosceles triangle. Let's take the angle as p

Since sum of angle in a triangle is 180°, then

p+ 75 +x = 180

p+75+75 = 180

p+150=180

p = 180-150

p = 30°

To get y:

Know that the y + p = 90° (right angled)

y + 30 = 90

y = 90-30

y = 60°

Hence x = 75° and y = 60°

b)Note that the triangle in the middle is an equilateral triangle. The sum of angle in a triangle is 180°

Hence all the angles are 60°

To get x;

Sum of angle on the straight line is expressed as;

40°+60°+x° = 180°

100°+x = 180°

x = 180°-100°

x = 80°

Also since the lines are parallel, the angle at the right corner of the triangle is also 40° (corresponding to that angle at the corner of the first triangle)

To calculate y;

Sum of angle in the triangle at the right is 180° hence;

x+y+40 = 180

80+y+40=180

120+y = 180

y = 180-120

y = 60°

Hence the value of x and y are 80° and 60° respectively.

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