Question

in the triangle below, ∠f is a right angle. suppose that m∠d = (4x + 22)° and m∠e = (3x + 33)°.
(a) write an equation to find x. make sure you use an \=\ sign in your answer.
equation:
(b) find the degree measure of each angle.
m∠d = °
m∠e = °
m∠f = °

Explanation:

Step1: Sum of acute angles = 90°

$(4x+22) + (3x+33) = 90$

Step2: Simplify left side

$7x + 55 = 90$

Step3: Solve for x

$7x = 90 - 55 = 35$
$x = \frac{35}{7} = 5$

Step4: Calculate $m\angle D$

$m\angle D = 4(5) + 22 = 20 + 22 = 42$

Step5: Calculate $m\angle E$

$m\angle E = 3(5) + 33 = 15 + 33 = 48$

Step6: Identify $m\angle F$

$m\angle F = 90$ (given right angle)

Answer:

(a) Equation: $\boldsymbol{(4x+22)+(3x+33)=90}$
(b)
$m\angle D = 42^\circ$
$m\angle E = 48^\circ$
$m\angle F = 90^\circ$