Question

The angles of a quadrilateral are (x+1), (5x + 4), (x – 2) and (3x + 7). Find all the angles of the quadrilateral. Also tell the type of quadrilateral.​

Answer 1

$\large{(x + 1) + (5x + 4) + (x - 2) + (3x + 7) = 60}$

$\large{x + 5x + x + 3x + 1 + 4 - 2 + 7 = 360}$

$\large{ \red {\fbox{10x + 10 = 360}}}$

$\large{ \pink{x = 35}}$

$\large \green{10x = 360 - 10}$

$\large \color{red}{ \colorbox{blue}{10x = 350}}$

$\large{ x = \frac{350}{10} }$

$\large{( x + 1) = 35 + 1 = 36}$

$\large{(5x + 4) = 5 \times 34+ 4 = 179}$

$\large{(x - 2) = 35 - 2 = 33}$

$\large{(3x + 7) = 3 \times 35 + 7 = 112}$

$\large{ \purple{ \bold{ \fbox{hence \: the \: angels \: are \: 36 \: \: 179 \: \: 33 \: \: 112}}}}$

hope its help u

Answer 2

Answer: The angles of the quadrilateral are 36°,179°,33°,112°.

Given: It is given that there is a quadrilateral with angles (x+1), (5x+4), (x-2) and (3x+7)

To Find: We need to find all the angles of the quadrilateral and also tell the type of quadrilateral.

Step-by-Step Explanation: We know that the sum of the angles of the quadrilateral is 360°.

Step 1: Calculating each angle of the quadrilateral:

(x+1)+(5x+4)+(x-2)+(3x+7) = 360°

⇒ 10x+10 = 360°

⇒ 10x = 350°

⇒ x = 35°

So, ∡A = x+1 = 35+1 = 36°

∡B = 5x+4 = 5*35 + 4 = 179°

∡C = x-2 = 35-2 = 33°

∡D = 3x+7 = 3*35 + 7 = 112°

Step 2: Checking the type of quadrilateral:

• Since, any of the angle is not equal to 90°, therefore this quadrilateral is neither a square nor a rectangle.
• Since, the opposite angles are not equal therefore this quadrilateral is neither a parallelogram nor a rhombus.
• Since, the sum of opposite angles of the quadrilateral is not 180°, therefore this quadrilateral is not a trapezium.

• Since, any two angles are not equal in the given quadrilateral, therefore we cannot find a pair of opposite angles which are equal, therefore this quadrilateral is not a kite.

Since, the given quadrilateral does not meet the criteria of any standard quadrilateral, therefore we cannot tell the type of quadrilateral.

To know more about the topic Geometry, refer to the links below:

https://brainly.in/question/5160593

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