Question

problem 15: △def is a right triangle and ∠e is a right angle. if m∠d = 8x - 1 and m∠f = 5x, find the measures of the angles of △def. after you enter your answer press go. m∠e = m∠d = m∠f =

Explanation:

Step1: Use angle - sum property of triangle

In $\triangle DEF$, $m\angle D+m\angle E + m\angle F=180^{\circ}$. Since $\angle E = 90^{\circ}$, we have $(8x - 1)+90 + 5x=180$.

Step2: Combine like - terms

Combine the $x$ terms and constants: $(8x+5x)+(90 - 1)=180$, which simplifies to $13x + 89=180$.

Step3: Solve for $x$

Subtract 89 from both sides: $13x=180 - 89$, so $13x = 91$. Then divide both sides by 13: $x=\frac{91}{13}=7$.

Step4: Find $m\angle D$

Substitute $x = 7$ into the expression for $m\angle D$: $m\angle D=8x - 1=8\times7 - 1=56 - 1 = 55^{\circ}$.

Step5: Find $m\angle F$

Substitute $x = 7$ into the expression for $m\angle F$: $m\angle F=5x=5\times7 = 35^{\circ}$.

Answer:

$m\angle E = 90^{\circ}$, $m\angle D = 55^{\circ}$, $m\angle F = 35^{\circ}$