Question

(a) Name all the different regular polygons in the figure. (b) Write the measures of angles of the rhombus.

Answer 1

Answer:

2 hexagon

1 square

1 rhombus

B) 30 degrees and 150 degrees

As in the middle all polygons together form 360, and all angles of square measure 90, and all angles of hexagon (equilateral) measure 120

So,

There are

2 angles measuring 120, 1 that is 90

Let smaller angle of rhombus =x

120 +120+90+x=360

330+x=360

X=30

As we know the opposite angles of rhombus are equal

So we can find the measure of other two angles of rhombus by angle sum property. Let the other two angles be equal to 2y

2y +30+30=360

2y=360-60

2y=300

Y=300/2

Y=150

Answer 2

Answer:

a)Hexagon, square, rhombus

b)opposite angles are congruent, and consecutive angles are supplementary.

All sides are congruent by definition.

The diagonals bisect the angles.

The answer can be found by applying these properties