The values of the angles in the diagram are:
A = 99°
B = 149°
C = 81°
D = x + 32°
E = 131°
F = 49°
G = 31°
H = 63°
I = 2x + 1°
J = 90°
K = 90°
Angles A and J are vertical angles, so they have the same measure of 90°.
Angles B and K are vertical angles, so they have the same measure of 90°
Angles A, B, C, D, and E form a straight angle, so they add up to 180°. Therefore, we have the following equation:
A + B + C + D + E = 180°
Substituting in the values that we already know, we get the following equation:
99° + 149° + 81° + x + 32° + 131° = 180°
Combining like terms, we get the following equation:
x = 180° - 494°
Solving for x, we get the following value:
x = -314°
However, angles cannot have negative measures. Therefore, the value of angle D is 180° + 314° = 494°.
Angles D and H are supplementary angles, so they add up to 180°. Therefore, we have the following equation:
D + H = 180°
Substituting in the value that we just found for angle D, we get the following equation
494° + H = 180°
Solving for H, we get the following value:
H = 180° - 494°
However, angles cannot have negative measures. Therefore, the value of angle H is 180° + 314° = 494°.
Angles C and G are supplementary angles, so they add up to 180°. Therefore, we have the following equation:
C + G = 180°
Substituting in the values that we know, we get the following equation:
81° + G = 180°
Solving for G, we get the following value:
G = 180° - 81°
Therefore, the value of angle G is 99°.
Angles I and F are supplementary angles, so they add up to 180°. Therefore, we have the following equation:
I + F = 180°
Substituting in the values that we know, we get the following equation:
2x + 1° + 49° = 180°
Combining like terms, we get the following equation:
2x = 130°
Dividing both sides by 2, we get the following value for x:
x = 65°
Therefore, the value of angle I is 2x + 1° = 131°.