Question

In the triangle, suppose that mD=(x+7), mZE-(4x-3), and mZF= (3x)".

Check
(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.
m2D-
m2E-
m2F-
X

Answer 1

(a) Equation: (x + 7) + (4x - 3) + (3x) = 180

(b) m ∠D = 29°, m ∠E = 85°, and m ∠F = 66°

Explanation:

(a): According to the triangle sum theorem, the sum of the interior angles of a triangle equals 180°. Thus, setting the sum of the angles equal to 180 allows us to find x:

m ∠D + m ∠E + m ∠F = 180

Equation: (x + 7) + (4x - 3) + (3x) = 180°

(b):

Step 1: First, we need to find x:

(x + 7) + (4x - 3) + (3x)

(x + 4x + 3x) + (7 - 3) = 180

8x + 4 = 180

8x = 176

x = 22

Step 2: Now we can plug in 22 for x for each expression representing the angle measures:

Plugging in 22 for x in ∠D expression:

m ∠D = (22 + 7)

m ∠D = 29°

Plugging in 22 for x in ∠E expression:

m ∠E = 4(22) -3

m ∠E = 88 - 3

m ∠E = 85°

Plugging in 22 for x in ∠F expression:

m ∠F = 3(22)

m ∠F = 66°

Optional Step 3: We can check that the sum of the three angles we've found equals 180:

29 + 85 + 66 = 180

114 + 66 = 180

180 = 180