Question

Two opposite angles in a rhombus measure (2x + 30°) and (5x – 18°) respectively. Find the measure of all the angles of the rhombus.​

Answer 1

Answer:

Since opposite angle of rhombus are equal ...

then,

(2x + 30°) = (5x – 18°)

2x + 30° = 5x – 18°

2x-5x=18°-30°

-3x=--12

x=4°

the two angles are:-

2(4)+30°=38°

the other two angles are:-

180°-38°=142°

measure of all the angles of the rhombus:-

measure of all the angles of the rhombus:-38°,142°,38°,142°

Answer 2

Step-by-step explanation:

we know that opposite angles in rhombus are equal

then,A.T.Q

2x+30=5x-18

30+18=5x-2x

48=3x

x=16

1st angle of rhombus =2x+30=2×16+30=32+30=62

2nd angle of rhombus =5x-18=5×16-18=80-18=62

we know that adjacent angles of rhombus are supplementary

Then,

2x+30 + 3 angle =180

3rd angle =180-62=118

opposite angles in rhombus are equal

Then

4th angle =3rd angle =118