Question

A rectangle has corners E, F, G, D, starting from top left and going clockwise. Point H is halfway between E and F. 2 lines are inscribed in the rectangle. One line goes from D to H and another goes from H to G. Angle E D H is (5 x) degrees and angle H D G is (4 x) degrees. Angles E D G and F G D are right angles.

What is the measure of AngleEDH?


10°

40°

50°

90°

Answer 1

50 degrees

Explanation:

The question says that A rectangle has corners E, F, G, D, starting from top left and going clockwise. Point H is halfway between E and F. 2 lines are inscribed in the rectangle. One line goes from D to H and another goes from H to G. Angle E D H is (5 x) degrees and angle H D G is (4 x) degrees. Angles E D G and F G D are right angles.

What is the measure of AngleEDH?

From the question above,a diagram of a rectangle with a triangle inscribed in it will appear and if angle EDH is 5x degrees and HDG is 4x degrees, and another look at the image you'd realize that the sum of this angles is 90(right angle) and from there we solve for X.

If 9X = 90

X = 10

Therefore angle EDH which has the shape of a right angle triangle and has the angle as 5x = 5 × 10

Angle EDH = 50 degrees

Answer 2

Angle EDH = 50°

Explanation:

The picture above is the rectangle formed from the illustration above. The angle EDH is given as 5x° and angle HDG is given as 4x° . The angles EDG and FGD are right angles . That means both angles are equivalent to 90° .

Angle EDH = 5x°

Angle HDG = 4x°

Angle EDG = 90°

Therefore,

5x + 4x = 90

9x = 90

divide both sides by 9

x = 90/9

x = 10°

Angle EDH = 5x = 5 × 10 = 50°