Question

Two adjacent angles are (2x+5) and (3x+10) find all angles of a parallelogram

Answer 1

we know that sum of adjacent angle in a parallelogram is 180.

(2x+5)+(3x+10)=180

2x+5+3x+10=180

5x +15=180

5(x+3)=180

x+3=180/5

x+3=36

x=36-3

x=33

∴the first angle is 2*33+5=66+5=71

 the second angle is 3*33+10=109.

since the opposite angles are equal in a parallelogram,two angles are 71°and the other two angles are 109°.

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Answer 2

The values of angles of the parallelogram are 75°, 105°,75° and 105°.

Given:

The adjacent angles are (2x+5) and (3x+10).

To Find:

All the angles of the parallelogram.

Solution:

To find all the angles of the parallelogram we will follow the following steps:

As we know,

The sum of adjacent angles of a parallelogram is 180°.

So,

The aim of angles (2x+5) and (3x+10) is 180°.

Now,

$(2x+5) + (3x+10) = 180$

$5x + 15 = 180$

$5x = 180 - 15 = 165$

$x = \frac{165}{5} = 35$

So, the angles are:

(2x+5) = (2×35 + 5) = 70 + 5 = 75°

(3x+10) = 3× 35 + 10 = 105°

Also,

Opposite angles of parallelograms are equal.

So, two angles are 75° and two are 105°.

Henceforth, the values of angles of the parallelogram are 75°, 105°,75° and 105°.

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