Problem 6, part c)
The tickmarks indicate the sides are the same length. This triangle is isosceles.
The two base angles are always opposite the congruent sides. One base angle is 25, so the other base angle must be 25 as well (base angles are congruent for isosceles triangles).
The three angles of this triangle are
25, 25 and 4x+2
Add those three angles up, set the result equal to 180, and solve for x
4x+2+25+25 = 180
4x+52 = 180
4x = 180-52
4x = 128
x = 128/4
x = 32 is the answer
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Problem 7, part a)
We use the same idea as with the last problem above. This works because this triangle is also isosceles (due to the tickmarks).
The three angles of this triangle are
(4x+1), (4x+1) and (5x-4)
note how (4x+1) shows up twice because it is a base angle
Add up those angles and set it equal to 180 to solve for x
(4x+1) + (4x+1) + (5x-4) = 180
13x - 2 = 180
13x = 180+2
13x = 182
x = 182/13
x = 14
Using this x value, we can find angle F
angle F = 5x-4
angle F = 5*14-4
angle F = 70-4
angle F = 66 degrees is the answer
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Problem 7, part b)
We'll use the x value found back in part a) above.
angle D = 4x+1
angle D = 4*14+1
angle D = 56+1
angle D = 57 degrees is the answer
Angle E is also 57, since D and E are congruent base angles
note how D+E+F = 57+57+66 = 180 to help confirm our answers