Question

find ( mangle deh ) and ( mangle feh ).
(10( x ) + 21)( ^circ ) ( f )
( h )
13( x )( ^circ ) ( d ) ( e )
( mangle deh = square^circ )
( mangle feh = square^circ )

Explanation:

Step1: Identify the right angle

From the diagram, $\angle DEF$ is a right angle, so $m\angle DEF = 90^\circ$. This means $m\angle DEH + m\angle FEH = 90^\circ$. Substituting the given expressions, we get $13x + (10x + 21) = 90$.

Step2: Solve for x

Combine like terms: $13x + 10x + 21 = 90$ → $23x + 21 = 90$. Subtract 21 from both sides: $23x = 90 - 21 = 69$. Divide by 23: $x = \frac{69}{23} = 3$.

Step3: Find $m\angle DEH$

Substitute $x = 3$ into $13x$: $m\angle DEH = 13(3) = 39^\circ$.

Step4: Find $m\angle FEH$

Substitute $x = 3$ into $10x + 21$: $m\angle FEH = 10(3) + 21 = 30 + 21 = 51^\circ$.

Answer:

$m\angle DEH = \boldsymbol{39}^\circ$
$m\angle FEH = \boldsymbol{51}^\circ$