Question

I already know y = 8, but I have no idea what the rest of the answers are, please help.

Answer 1

See image

Explanation:

If you put the 8 in for y, then all of a sudden, hurray there's enough info to keep going. It is an isosceles triangle which means two sides are the same. That also means that the two angles opposite the two equal sides are also equal. That's how we know the unmarked angle is also 4x

"Triangle Angle Sum" means to use the fact that all the angles in a triangle added up equals 180°. So add up all the angles, set equal to 180 and solve. To find the angle measures just pop in the x=18 to calculate. See image.

Answer 2

• See below

Explanation:

a)

As per diagram DF = EF, substitute values to solve for y:

• 2y + 5 = 21
• 2y = 16
• y = 8

b)

Angles D and E marked as equal, the sum of interior angles is:

• D + E + F = 180

Substitute to get:

• 4x + 4x + 2x = 180

c)

Solve for x:

• 4x + 4x + 2x = 180
• 10x = 180
• x = 18

d)

Angle F is 2x:

• m∠F = 2x = 2*18 = 36°

e)

Angle D is 4x:

• m∠D = 4x = 4*18 = 72°