Question

find the missing value of x
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Answer 1

Solution:-

let ∠1 = x , ∠2 = 80⁰ , ∠3 = 60⁰ and ∠4 is formed right angle so ∠4 = 90⁰

We know that

All angle sum of the quadrilateral is 360°.  

= ∠1 + ∠2 + ∠3 + ∠4 = 360⁰

=> x + 80⁰ + 60⁰ + 90⁰ = 360⁰

=> x + 140⁰ + 90⁰ = 360⁰

=> x + 230⁰ = 360⁰

=> x = 360⁰ - 230⁰

=> x = 130⁰

So ∠1 = 130⁰

Let's verify our answer

∠1 + ∠2 + ∠3 + ∠4 = 360⁰

=> x + 80⁰ + 60⁰ + 90⁰ = 360⁰

=> 130⁰ + 80⁰ + 60⁰ + 90⁰ = 360⁰

=> 210⁰ + 150⁰ = 360⁰

=> 360⁰ = 360⁰

LHS = RHS

More information about quadrilateral

Quadrilateral are a special type of polygon. As with triangles and other polygons

quadrilaterals have special properties and can be classified by characteristics of their angles and sides.

All quadrilaterals are coplanar and have two diagonals.

Quadrilaterals may be drawn in a "convex" form or a "concave" form.

The quadrilaterals we will be using will be convex, where the diagonals lie within the figure.

A concave quadrilateral contains an angle greater than 180º