Question

In a parallelogram if the measure of two adjacent angles are in the ratio of 4 :5 find all the angles​

Answer 1

Answer:

80° and 100°

Step-by-step explanation:

let the two angles be 4x and 5x.

Then the following steps are given in the picture

Answer 2

★ Given :

• Two adjacent to of a parallelogram are in the ratio 4 : 5.

★ To Find :

• Measure of all the angles of parallelogram

★ Solution :

Let us consider the two adjacent angles be 4x and 5x.

Now,

• Sum of adjacent angles of a parallelogram = 180°.

Equation :

$\underline{ \boxed{ \bold{ \red{5x + 7x = 180}}}} \: \: \bigstar$

• According to the question.

Let's solve the above equation to find the value of x.

$:\implies \sf\:4x + 5x = 180$

$:\implies \sf\:9x = 180$

$:\implies\sf\: x = \cfrac{ \cancel{180}}{ \cancel{9}}$

$:\implies \underline {\boxed{\bold{ \green{x = 20}}}} \: \: \: \: \: \: \dag$

Hence, x = 20°,Now angles =4x = 80° and 5x = 100°.

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More to Know :

• Quadrilateral - A simple closed figure bounded by four line segments.

• Parallelogram - It is a quadrilateral in which

1. Opposite sides are equal and parallel.
2. Opposite angles are equal.
3. Sum of adjacent angles = 180°.