Question

Find m∠DEH and m∠FEH.

Answer 1

The figure is a right angle that is 90°. Using this,

(10x+21)+(13x)= 90°

10x+21+13x= 90°

23x= 90-21

23x= 69°

x= 69/23

x= 3°

<DEH= 13x= 13×3 = 39°

<FEH= 10x+21 = 10×3+21 = 51°

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Answer 2

Given:

∠FEH = $(10x+21)$°

∠DEH = $13x$°

∠FED = 90°

To find:

The value of ∠DEH and ∠FEH.

Solution:

From the given figure, we can observe that,

∠FED forms a 90°, so the sum of the angles formed at point E will be 90°.

So, we can write,

∠FEH + ∠DEH = ∠FED

⇒$(10x+21)$° + $13x$° = 90°

⇒$23x+21=90$

⇒$23x=69$

⇒$x=3$

So, we put the value of $x$ to find the respective values of the angles, as follows,

∠FEH = $(10x+21)$°

=$(30+21)$°

=51°

∠DEH = $13x$°

=39°

Hence, ∠FEH is 51° and ∠DEH is 39°.