ABCDE is a regular pentagon. Sides AE and ED of the pentagon are exten...
Step 1: Understand the question and draw inferences
To find –x°+ y°
Given – ABCDE is a regular pentagon.
This means, all sides of the pentagon are equal.
Therefore, AB = BC
In triangle ABC, two sides are equal.
Therefore, triangle ABC is an isosceles triangle.
Since angles opposite to equal sides are also equal,
Angle BAC = Angle ACB = x°
Let Angle ABC = i°
Therefore, by Angle Sum Property,
2x° + i° = 180° . . . (1)
Now, considering the right triangle EFG,
Let angle FEG = e°
Therefore, by Angle Sum Property,
e° + y° + 90° = 180°
e° + y° = 90° . . . (2)
Step 2: Finding the required values
We know that for interior angle of an n-sided regular polygon =
So, for n = 5, value of each interior angle =
Therefore, i° = 108° . . . (3)
Also, we know that Exterior Angle of an n-sided regular polygon = 360on
So, for n = 5, the value of each exterior angle = 360o/5 = 72°
Notice that Angle FEG is an exterior angle of the regular pentagon.
Therefore, e° = 72° . . . (4)
Step 3: Calculating the final answer
From (1) and (3), we get:
2x° + 108° = 180°
Solving this equation, we get x° = 36°
From (2) and (4), we get:
72° + y° = 90°
y° = 18°
Thus, x° + y° = 36° + 18° = 54°
Correct Choice -C