Answer:
The measure of the three angles are;
The first angle is 62°
The second angle is 28°
The third angle is 90°
Step-by-step explanation:
The given information are;
The shape of the parking lot = Triangular
Let the angles of the triangle be given as follows
First angle = A
Second angle = B
Third angle = C
The given triangle interior angle dimensions are;
A = 6 + 2× B
C = A + B
However, we have;
A + B + C = 180° (Angle sum property for a triangle)
Therefore;
A + B + C = 180° gives;
C + C = 180° (Transitive property)
2·C = 180°
C = 180°/2 = 90°
C = 90°
However, C = A + B therefore;
90° = A + B and, A = 6 + 2 × B, we get;
A + B = 90° (Symmetric property)
6 + 2× B + B = 90° (Substitution property)
6 + 3·B = 90°
3·B = 90° - 6° = 84°
B = 84°/3 = 28°
B = 28°
From, A = 6 + 2 × B, we have;
A = 6 + 2 × 28° = 62°
A = 62°
First angle = A = 62°
Second angle = B = 28°
Third angle = C = 90°
The measure of the three angles are;
First angle is 62°
Second angle is 28°
Third angle is 90°.
