Question

Find the unknown sizes of angles of figures.

Answer 1

Answer:

w=130

z=130

x=25

y=25

z=130 ,because in a triangle total angle=180, n there are two other angles, 25°, 25° so 180-(25+25) =130°

And as we know in parallelogram, opposite angles are equal so, z=w=130°

n in parallelogram corresponding angles are equal so, x=25=y

Answer 2

Answer:

Let us name it quadrilateral ABCD.

ABCD is a parallelogram(opposite sides are parallel)-(1)

In triangle ABC,

angle CAB=angle BCA= 25°

AB=BC( sides opposite to equal angle or isosceles triangle property)-(2)

AB=DC and CB=DA( From 1)

AB=DC and AB=DA(From 2)

Finally we get, DC=DA. This also means that triangle ADC is isosceles.

Angle x= Angle y( angles opposite to equal sides)-(3)

So now in triangle ABC,

Angle CAB + angle ABC + Angle BCA=180° (angle sum property of triangle)

25°+z+25°=180°

50°+z=180°

z=180°-50°

z=130°

w=z( opposite angles in a parallelogram are equal)

w=130°

So now in triangle ADC,

Angle DAC+ Angle ADC+ Angle DCA=180° ( angle sum property of a triangle)

y+w+x=180°

x+x+130°=180°( From 3)

2x=180°-130°

2x=50°

x=50°/2

x=25°=y