5. The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram .
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Answers
Step-by-step explanation:
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Answer :
›»› The measure of each of the angles of the parallelogram are 108°, 72°, 108° and 72°.
Given :
- The measures of two adjacent angles of a parallelogram are in the ratio 3:2.
To Find :
- The measure of each of the angles of the parallelogram.
Solution :
Let,
The measure of two adjacent angle be "3x" and "2x" respectively.
As we know that
The sum of the measure of adjacent angle is 180°.
→ 3x + 2x = 180
→ 5x = 180
→ x = 180/5
→ x = 36
Therefore,
→ The measure of first angle = 3x
→ The measure of first angle = 3 * 36
→ The measure of first angle = 108°
→ The measure of second angle = 2x
→ The measure of second angle = 2 * 36
→ The measure of second angle = 72°
→ First angle = third angle (Opposite angles).
→ Second angle = fourth angle (Opposite angles).
→ 108° = 108° (Opposite angles).
→ 72° = 72° (Opposite angles).
║Hence the measure of each of the angles of the parallelogram are 108°, 72°, 108° and 72°.║
Verification :
Sum of all angles of parallelogram is 360°
→ 108 + 72 + 108 + 72 = 360
→ 180 + 108 + 72 = 360
→ 180 + 180 = 360
→ 360 = 360
Here, LHS = RHS
Hence Verified !