Final answer:
To find X and Y, two equations were derived from the angles of the isosceles triangle, and it was assumed the angles corresponding to 8y+10 and 3x+8 are equal. Solving the equations, we found X = 18.5 and Y = 6.6875.
Step-by-step explanation:
The subject of this question is to find the values of X and Y in an isosceles triangle where one angle is 53°, another is represented by the expression 8y+10, and the third angle is represented by the expression 3x+8.
Since the sum of angles in a triangle is always 180°, we can set up an equation:
53 + (8y+10) + (3x+8) = 180
This is the equation we need to solve to find X and Y. However, because this is an isosceles triangle and two angles are equal, we can deduce which angles are equal based on the fact that typically only one angle in a triangle is significantly larger than 53°, which might be the given angle.
Without loss of generality, we can assume the two angles formed by 8y+10 and 3x+8 should be equal. Thus, we have two equations:
- 8y+10 = 3x+8
- 53 + (8y+10) + (8y+10) = 180
Solving these equations, we find:
- 8y+10 = 3x+8 (Equation 1)
- 16y + 73 = 180 (Simplified second equation)
Next, solve for y in the second equation:
16y = 107
y = 107 / 16
y = 6.6875
Having found the value of y, we can now backtrack to Equation 1 to solve for x:
8(6.6875) + 10 = 3x + 8
53.5 + 10 = 3x + 8
3x = 55.5
x = 55.5 / 3
x = 18.5
The values of X and Y in the isosceles triangle are X = 18.5 and Y = 6.6875.