Question

Find the measure of the numbered angles in rhombus ABCD

Answer 1

Answer:

see the explanation

Step-by-step explanation:

we know that

In a Rhombus opposite angles are congruent and consecutive angles are supplementary

The diagonals are perpendicular and bisect the angles

so

step 1

Find the measure of angle 4

we know that

$m\angle 4=27^o$ --->by the diagonals bisect the angles

step 2

Find the measure of angle 1

we know that

$m\angle 1=27^o$ ----> by opposite angles are congruent

step 3

Find the measure of angle 2

we know that

$m\angle 1=m\angle 2$ ----> by the diagonals bisect the angles

so

$m\angle 2=27^o$

step 4

Find the measure of angle 3

we know that

$m\angle 3=90^o$ ----> by the diagonals are perpendicular

step 5

Find the measure of angle 5

we know that

$m\angle 5+27^o=90^o$ ----> by complementary angles

$m\angle 5=90^o-27^o=63^o$

step 6

Find the measure of angle 6

we know that

$m\angle 6=m\angle 5$ ----> by the diagonals bisect the angles

$m\angle 6=63^o$