Question

Can someone please help me with 3,4,5,6 pleaseeee!

Answer 1

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°