Question

two adjacent angle of a parallelogram are in the ratio 5:7 find the measure of all the angle​

Answer 1

Answer

• Measure of all the angles = 75°, 115°, 75° and 105°.

Given

• Two adjacent to of a parallelogram are in the ratio 5 : 7.

To Find

• Measure of all the angles of parallelogram.

Step By Step Explanation

Assumption :

Let us consider the two adjacent angles be 5x and 7x.

Now,

Sum of adjacent angles of a parallelogram = 180°.

Equation :

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

Solution of Equation :

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

$\longmapsto \sf5x + 7x = 180 \\ \\ \longmapsto \sf12x = 180 \\ \\ \longmapsto \sf x = \cfrac{ \cancel{180}}{ \cancel{12}} \\ \\ \longmapsto \underline {\boxed{\bold{ \green{x = 15}}}} \: \: \: \: \: \: \dag$

Hence, x = 15°, Now angles => 5x = 75° and 7x = 105°.

We know that :

Opposite angles of parallelogram are equal.

Therefore, measure of all the angles are 75°, 105°, 75° and 105°.

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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°.

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