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Maths-

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Easy

Question

Quadrilateral ABCD is shown. Which equation shows how the measures of the angles of the quadrilateral are related?

$x + 90 + (2 x - 5) + (x + 35) = 360$
$4 (x + 90 + (2 x - 5) + (x + 35)) = 360$
$x + (2 x - 5) + (x + 35) = 360$
$4 (x + (2 x - 5) + (x + 35)) = 360$

The correct answer is: $x plus 90 plus left parenthesis 2 x minus 5 right parenthesis plus left parenthesis x plus 35 right parenthesis equals 360$

The total of all four angles of any quadrilateral is $2 pi equals 360 degree$ . According to the diagram, the $angle B$ is a right angle, i.e., $angle B equals 90 degree$ .
Explanation:
Step 1 of 2:
In the given quadrilateral ABCD, the measures of the four angles are given by $angle A equals x degree$ , $angle B equals 90 degree$ , $angle C equals open parentheses 2 x minus 5 close parentheses degree$ and $angle D equals open parentheses x plus 35 close parentheses degree$ .
Step 2 of 2:
$therefore$ We have $x degree plus 90 degree plus open parentheses 2 x minus 5 close parentheses degree plus open parentheses x plus 35 close parentheses degree equals 360 degree$
Final Answer:
So, the equation shows how the measures of the angles of the quadrilateral are related is— $x plus 90 plus open parentheses 2 x minus 5 close parentheses plus open parentheses x plus 35 close parentheses equals 360$ .

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