Question

in the above figure, a quadrilateral is formed by joining two triangles. find the sum of all the angles of a quadrilateral.
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Answer 1

Answer:

Given-triangle ABC and BCD

SUM OF ALL ANGELS OF TRIANGLE ARE 180 . THEREFORE ALL ANGLES ARE OF 360 AND THEREFORE SUM OF ALL ANGLES OF QUADRILATERAL ARE 360

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Sum of all the angles of quadrilateral ABCD = 360°

$\bold{\underline{\underline{Step\:-\:by\:step\:explanation:}}}$

Given :

• ◾ABCD formed from two triangles.

1. Δ ABC
2. Δ BDC

To find :

• Sum of all the angels of quadrilateral ABCD.

Solution :-

We know that :-

• Sum of measures of all angles in a triangle is 180°

In Δ ABC,

Let angle A = x °

Let angle B = x°

Let angle C = x°

$\rightarrow$ $\bold{A+B+C=180}$

$\rightarrow$ $\bold{x+x+x}$ = 180

$\rightarrow$ $\bold{3x}$ = 180

$\rightarrow$ $\bold{x}$ = $\bold{\dfrac{180}{3}}$

$\rightarrow$ $\bold{x}}}$ = $\bold{60}$

•°• Angle A = x = 60

Angle B = x = 60

Angle C = x = 60

In Δ BDC,

Let angle B = x°

Let angle D = x °

Let angle C = x°

$\rightarrow$ $\bold{B+D+C}$ = 180°

$\rightarrow$ $\bold{x+x+x}$ = 180

$\rightarrow$ $\bold{3x}$ = 180

$\rightarrow$ $\bold{x}$ = $\bold{\dfrac{180}{3}}$

$\rightarrow$ $\bold{x}$ = $\bold{60}$

•°• Angle B = x = 60°

Angle D = x = 60°

Angle C = x = 60°

The quadrilateral ABCD is formed from the triangles ABC and BDC whose sum of measures of all angles is 180° respectively.

•°• Quad. ABCD = Δ ABC + Δ BDC

Quad. ABCD = 180 + 180

Quad. ABCD = 360 °