If it is 2D....let's label the figure like this:
△ABE is an equilateral triangle, so every interior angle is 60°, and so
m∠EAB = 60°
m∠ABE = 60°
We are given that
m∠EBC = 90°
Now we can determine that
m∠ABC = 60° + 90°
m∠ABC = 150°
△ABC is an isosceles triangle. so base angles are congruent, and so
m∠BCA = m∠BAC
The sum of the measures of the interior angles in a triangle is 180°, so
m∠BAC + m∠BCA + m∠ABC = 180°
Substitute m∠BAC in for m∠BCA and 150° in for m∠ABC
m∠BAC + m∠BAC + 150° = 180°
Combine like terms
2(m∠BAC) + 150° = 180°
Subtract 150° from both sides of the equation.
2(m∠BAC) = 30°
Divide both sides of the equation by 2
m∠BAC = 15°
In the same way, we can determine that
m∠EAD = 15°
Then
m∠DAC = m∠EAB - m∠EAD - m∠BAC = 60° - 15° - 15° = 30°
Please explain more.
Is the a 2d object or is it a representation of a 3D object.
What object is it?
If it is 2D....let's label the figure like this:
△ABE is an equilateral triangle, so every interior angle is 60°, and so
m∠EAB = 60°
m∠ABE = 60°
We are given that
m∠EBC = 90°
Now we can determine that
m∠ABC = 60° + 90°
m∠ABC = 150°
△ABC is an isosceles triangle. so base angles are congruent, and so
m∠BCA = m∠BAC
The sum of the measures of the interior angles in a triangle is 180°, so
m∠BAC + m∠BCA + m∠ABC = 180°
Substitute m∠BAC in for m∠BCA and 150° in for m∠ABC
m∠BAC + m∠BAC + 150° = 180°
Combine like terms
2(m∠BAC) + 150° = 180°
Subtract 150° from both sides of the equation.
2(m∠BAC) = 30°
Divide both sides of the equation by 2
m∠BAC = 15°
In the same way, we can determine that
m∠EAD = 15°
Then
m∠DAC = m∠EAB - m∠EAD - m∠BAC = 60° - 15° - 15° = 30°