Answer:
3) m∠E = 102°
4) m∠V = 41°
5) x = 9
6) m∠J = 77°
Step-by-step explanation:
3) Find m∠E:
∠DFE and ∠GFH are opposite angles, so they have equal measures.
Now you know have 3 expressions for the angle measures of ΔGFH
Write an equation and solve for x:
(10x + 3) + (13x - 5) + 90 = 180
combine like terms:
23x + 88 = 180
subtract 88:
23x = 92
divide by 23:
x = 4°
Now that you have the value of x, you can evaluate both expressions given for ΔDFE:
6(4) + 11 = 35°
10(4) + 3 = 43°
Solve for the missing angle:
35 + 43 + m∠E = 180
m∠E + 78 = 180
m∠E = 102°
4) Find m∠V
ΔRST is an equilateral triangle (all sides are equal)
An equilateral triangle has 3 equal angles:
180 ÷ 3 = 60°
∠STR and ∠UTV are supplementary (add up to 180°):
m∠STR + m∠UTV = 180
m∠UTV + 60 = 180
∠UTV = 120°
Now that you have this angle, you can calculate the value of x:
120 + (5x + 6) + (4x - 9) = 180
9x + 117 = 180
9x = 63
x = 7
Now you can calculate the measure of ∠V
m∠V = 5(7) + 6 = 41°
5) Find the value of x
ΔPQR is an isosceles triangle (2 sides are equal)
In an isosceles triangle, the base angles are congruent.
Write an equation and solve for x:
29 + 29 + (8x - 14) = 180
8x + 44 = 180
8x = 136
x = 17
6) Find m∠J
Same as the last one, base angles are congruent.
Write an equation and solve for x:
(8x + 5) + (8x + 5) + (5x - 19) = 180
21x - 9 = 180
21x = 189
x = 9
Calculate the measure of ∠J:
m∠J = 8(9) + 5 = 77°
then there is the imaginary part, and the real part