Simple angle question

[tex]Simple angle question[/tex]

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Simple angle question

[tex]Simple angle question[/tex]

Your answer should be “b” i truly hope i could ! good luck (:

see explanation

Step-by-step explanation:

Nicole has the correct equation

To find ∠ F use the Sine rule, that is

The ratio of the sine of an angle to the side opposite is equal to the ratio of the sine of another angle to the side opposite.

Matthew and Leah have mixed up the sine of an angle with the incorrect opposite side.

Following on with Nicole's solution

[tex]\frac{sin100}{27}[/tex] = [tex]\frac{sinF}{19}[/tex] ( cross- multiply )

27 × sinF = 19 × sin100° ( divide both sides by 27 )

sinF = [tex]\frac{19sin100}{27}[/tex] ≈ 0.6930, thus

F = [tex]sin^{-1}[/tex] (0.6930 ) ≈ 43.9° ( to 1 dec. place )

see below

Angle ACE = DCE since they are vertical angles

Angle A = Angle E parallel lines cut by a transversal form congruent alternate interior angles

Angle B = Angle D parallel lines cut by a transversal form congruent alternate interior angles

When all three angles are equal, the triangles are similar.

We can use ratios to find DE

DE CE

=

AB AC

DE 8

=

12 10

Using cross products

10 DE = 8*12

10 DE = 96

Divide by 10

DE = 9.6

I’m pretty sure the answer is Angel EAF

The answer is angle EAF

47

step-by-step explanation:

1) they are similar by AAA postulate

2) 9.6 cm

Explanation:

Triangles CAB and CED are similar

because:

1) both have the same angle C

(vertically opposite angles)

2) Angle A = Angle E

(alternate angles)

3) Angle B = Angle D

(alternate angles)

CA/CE = AB/ED

10/8 = 12/DE

DE = 12 × 8/10

DE = 9.6

112°

Step-by-step explanation:

Angle DAB and angle EDC are congruent b/c they are corresponding angles. Triangle CDE is isosceles so angle ECD is congruent to angle EDC.

Angle DEC = 180° - (2x34°) = 112°