Question

if 3 angles of a quadrilateral are 100 degree, 75 degree and 105 degree then the measurement of fourth angle is ​

Answer 1

Given:-

The angles are:-

• 100°
• 75°
• 105°

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Need to find:-

• The fourth angle = ?

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Soluton:-

Need to know:- The sum of four angles of a quadrateral = 360°

Now let the unknown angle be = x

Then,

100° + 75° + 105° + x = 360°

→ 175° + 105° + x = 360°

→ 280° + x = 360°

→ x = 360° - 280°

→ x = 80°

• Therefore the fourth angle is equal to 80°

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Knowledge cell:-

• Sum of all interior Angeles of a quadrateral = 360°

• Sum of all interior Angeles of a triangle = 180°

• Sum of all interior Angeles of a Pentagon = 540°

• Sum of all interior angles of a hexagon = 720°

Answer 2

$\large\underline\blue{\bold{Given \: Question :- }}$

• If 3 angles of a quadrilateral are 100 degree, 75 degree and 105 degree then the measurement of fourth angle is

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$\bf \:\large \red{AηsωeR : } ✍$

$\large\underline\blue{\bold{Given :- }}$

$\begin{gathered}\begin{gathered}\bf 3 \: angles \: of \: quadrilateral \: = \begin{cases} &\sf{100°} \\ &\sf{75°} \\ &\sf{105°} \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{To \: Find :- }}$

• Fourth angle of a quadrilateral

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$\large\underline\blue{\bold{Understanding \: the \: Concept :- }}$How to find the missing angle of a quadrilateral?

We know, The sum of all four angles of the quadrilateral is 360°. To find the fourth angle or the missing angle in a quadrilateral, when the measurements of three angles of a quadrilateral are known, then subtract the sum of three angles from 360° to calculate the missing angle.

Lets do it!!!

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$\large\underline\blue{\bold{Solution :- }}$

$\sf \: Let \: the \: fourth \: angle \: of \: the \: quadrilateral \: be \: x.$

$\bf \:  ⟼ We \: know \: that$

$\sf \: Sum \: of \: all \: angles \: of \: a \: quadrilateral \: is \: 360°.$

$\sf\implies \: 100° + 105° + 75° + x = 360°$

$\sf \: ⇒ 280° + x = 360°$

$\sf \: ⇒ x = 360° - 280°$

$\sf \: ⇒ x = 80°$

▪︎ Therefore, the measure of the fourth angle of the quadrilateral is 80°

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$\large {\bf \: ⟼ Explore \: more } ✍$

Quadrilateral Definition

• A quadrilateral is a plane figure that has four sides or edges, and also have four corners or vertices. Quadrilaterals will typically be of standard shapes with four sides like rectangle, square, trapezoid, and kite or irregular and uncharacterized.

If ABCD is a quadrilateral then it will have

• Four sides: AB, BC, CD, and DA
• Four vertices: Points A, B, C, and D
• Four angles: ∠ABC, ∠BCD, ∠CDA, and ∠DAB
• ∠A and ∠B are adjacent angles
• ∠A and ∠C are the opposite angles
• AB and CD are the opposite sides
• AB and BC are the adjacent sides

Types of Quadrilaterals

There are many types of quadrilaterals. As the word ‘Quad’ means four, all these types of a quadrilateral have four sides, and the sum of angles of these shapes is 360 degrees.

• Trapezium
• Parallelogram
• Squares
• Rectangle
• Rhombus
• Kite

Another way to classify the types of quadrilaterals are:

• Convex Quadrilaterals: Both the diagonals of a quadrilateral are completely contained within a figure.
• Concave Quadrilaterals: At least one of the diagonals lies partly are entirely outside of the figure.
• Intersecting Quadrilaterals: Intersecting quadrilaterals are not simple quadrilaterals in which the pair of non-adjacent sides intersect. This kind of quadrilaterals are known as self-intersecting or crossed quadrilaterals

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