Question

How to solve? Help and or guide/answers???

Answer 1

First one: x would be equal to 8 because the angles opposite sides 8 and x are congruent (isosceles triangle)

Second one: x is 75° because the sides opposite x and 75° are congruent (isosceles triangle)

Third one: This is an equilateral triangle since all the sides are equal. In equilateral triangles, every angle is 60° because 60*3=180. So both x and y are 60°

Fourth one: We know that all three angles in a triangle add to 180°. And we also know that the last unlabled angle would be equal to x because this is an isosceles triangle. So we can write
x+x+38=180 (combine like terms)
2x+38=180 (subtract 38 from both sides)
2x=142 (divide both sides by 2)
x=71°

Fifth one: This is an equilateral triangle so all the angles are congruent and add to 180. So we can write
3(4x+12)=180 (distribute)
12x+36=180 (subtract 36 from both sides)
12x=144 (divide both sides by 12)
x=12

Last one: Since the two given angles are opposite congruent sides, these angles are equal. Therefore, we can just make each of these angles 3x to solve for x first. And since we know the last angle is 90° we can write
3x+3x+90=180 (combine like terms)
6x+90=180 (subtract 90 from both sides)
6x=90 (divide both sides by 6)
x=15
So the angle 3x would be 3*15 or 45. 
So we can set 45 equal to y+7 and solve for y
y+7=45 (subtract 7 from both sides)
y=38

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