Question

the fourth angle of a quadrilateral are equal. find the measure of each angle.​

Answer 1

Answer:

90°

Step-by-step explanation:

If the four angles of a quadrilateral ABCD are equal,

then,

Let the common multiple be 'x'

According to given condition,

A=B=C=D=x

therefore,

angle(A+B+C+D)=360°

(x+x+x+x)=360°

4x=360

x=360/4

x=90

A=B=C=D=x=90°

Answer 2

Correct question:

Four angles of a quadrilateral are

equal.Then find the value of each angle

Explanation:

$\sf consider \: quadrilateral \: ABCD$

According to the question,

$\bullet \sf \angle A=\angle B=\angle C=\angle D$

$\sf let \: \angle A=\angle B=\angle C=\angle D=x$

we know that

$\boxed{\sf sum \: of \: all \: angles \: in \: a \: quadrilateral=360\degree}$

Putting in the values

$\longrightarrow \sf \: \angle \: A + \angle B + \angle \: C + \angle \: D = 360 \degree \\ \\ \longrightarrow \sf x + x + x + x = 360 \\ \\ \longrightarrow \sf 4x = 360 \\ \\ \longrightarrow \sf x = \dfrac{360}{4} \\ \\ \longrightarrow \boxed{ \sf x = 90 \degree }</p><p>$

$\sf \angle A=\angle B=\angle C=\angle D=x=90\degree$

All angles in quadrilateral are equal and 90°

Therefore,the given quadrilateral is a rectangle