The adjacent angles o a rhombus are in the ratio 3 : 2. Find all the angles of the rhombus. PLEASE TELL THE ANSWER WHICH CALCULATIONS.
Answers
Answer:
Let the adjacent angles of the rhombus be 2x and 3x. We know that the sum of the measures of the adjacent angles is equal to 180°. AD = DC = 3 × 36° = 108°. Hence , the angles of the rhombus are 72° , 108° , 72° and 108°.
All the angles of the given rhombus will be:
two opposite angles = 108°, and
other two opposite angles = 72°.
Given,
The adjacent angles of a rhombus are in the ratio of 3:2.
To find,
All the angles of the rhombus.
Solution,
Firstly, let the two adjacent angles of the given rhombus be 3x and 2x.
Now, as we know that the adjacent angles of a rhombus are supplementary. It means,
the sum of two adjacent angles of a rhombus = 180°.
Since we assumed that adjacent angles for the given rhombus are 3x and 2x. So,
3x + 2x = 180
⇒ 5x = 180
⇒ x = 36.
From the above value of x, the 2 adjacent angles can be determined as,
1st angle, 3x = 3(36) = 108°,
2nd angle, 2x = 2(36) = 72°.
Thus, the two adjacent angles of the rhombus will be 108° and 72°.
Further, the angles of the opposite vertices of a rhombus are equal.
So, the other two adjacent angles will also be 108° and 72°.
Therefore, all the angles of the given rhombus will be:
two opposite angles = 108°, and
other two opposite angles = 72°.