need math help in finding a variables angle in the given triangles?

three rules you will need for the triangles:

1) if you extend the edge of a triangle, the exterior angle = the sum of the opposite 2 angles

2) sum of the interior angles of a triangle = 180

3) base angles of an isosceles triangles are congruent

3 rules for these particular quadrangles (4-sided)

4) opposite angles in a parallelogram are congruent

5) when 2 parallel lines are cut by a transversal the sum of the interior angles = 180

6) sum of the angles in a quadrilateral = 360

a) use rule 1

b) find the lower 2 interior angles first... 180 - 100 & 180 - 135.... then use rule 1

d) find the right interior angle... 180 - 150... then use rule 1

f) find the left and right interior angles... 360 - 330 & 180 - 115.... then the triangle with angle z IS an isosceles triangle so you can use rule 3 then rule 2 to actually get angle z... then find the other side of angle z... 180 - z ... now rule 2 to figure out y

c) you have two sets of parallel lines crossing each other so you have a parallelogram... use rule 4

e) use rule 5 to find the blank angle then rule 6

a) Use the exterior angle property.

70°+50°= x

120°=x

b) Here, you can apply the exterior angle property. But first you need to find the two angles inside the triangle which will be opposite to d.

Let's name the angle adjacent to 100° "x" and the one adjacent to 135° "y".

100° and x form a linear pair. So,

100°+x=180

x= 80°........................(i)

135° and y also form a linear pair. So,

135°+y=180

y=45°......................(ii)

Using (i) and (ii) in exterior angle property:

80°+45°=d

125°=d

c)The figure is a parallelogram i.e it has 2 pairs of parallel sides. In parallelograms opposite angles are equal. So,

x is opposite to 70°. Hence,

x= 70°

d)Use the exterior angle property.

b+100°=150°

b=50°

e) The lines with arrows on them are parallel. This means that 100° and k form a pair of co-interior angles.Co-interior angles are supplementary. So,

100°+k=180°

k=80°

f) The lines with dashes on them are equal in length. Let's call them x. Use the exterior angle property.

x+x=115°

2x=115°

x=57.5°

Using the angle sum property of triangles we get;

z+x+x=180°

z+2x=180°

z+115°=180°

z= 65°

In the smaller triangle:

The angle adjacent to z and z form a linear pair. Let's call the adjacent angle "a".

z+a=180°

65+a=180

a=115°........................(I)

The reflex angle is of 330°. The remaing angle is of:

360°-330°=30°.........................(II)

Using angle sum property in the smaller trianle:

a+30°+y=180°

115°+30+y=180°

145°+y=180°

y=35°

All 3 angles in a triangle add up to 180 degrees. In A you are looking for the supplementary angle of the angle not listed. So 70+50= 120 in order to get to 180 for the interior angles of the triangle the missing angle must be 60.

The adjacent angle to 60 is 120 because 120+60 = 180. Hope this helps