Question

5. The adjacent angles of a parallelogram are
in the ratio of 1:2. Find the measure of the
angles
(5 marks)​

Answer 1

Answer:

The angles are 60 and 120

Step-by-step explanation:

Ratio of angles - 1:2

Let the angles be x and 2x

Adjacent angles in a parallelogram are supplementary

x + 2x = 180

3x = 180

x = 180/3

x = 60

Therefore, the angles are 60 and 120

Answer 2

Given -

• Ratio of adjacent sides is 1:2

To find -

• Measures of the angles.

Solution -

In the question, a parallelogram is given, and their adjecent sides are in the ratio 1:2, and we are asked to find the measures of the angles. As we know, that the sum of adjacent angles of a parallelogram is equal to 180°, from this we are going to solve the problem.

So -

Let the common ratio be termed as x

1 = 1x or we take it simply as x = angle A

2 = 2x = angle b

On substituting the values -

$\longrightarrow$ x + 2x = 180°

$\longrightarrow$ 3x = 180°

$\longrightarrow$ x = $\sf\cancel\dfrac{180}{3}$

$\longrightarrow$ x = 60°

Measures of angles -

Angle A = x = 60°

Angle B = 2 × x = 2 × 60° = 120°

Verification -

Sum of adjacent angles = 180°

$\longrightarrow$ Angle A + Angle B = 180°

$\longrightarrow$ 60° + 120° = 180°

$\longrightarrow$ 180° = 180°

$\therefore$ Measures of x and 2x are 60° and 120°

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