The value of ∠x is 24°
The measure of ∠1 is 101°
The measure of ∠2 is 79°
The measure of ∠3 is 101°
The measure of ∠4 is 101°
The measure of ∠5 is 79°
The measure of ∠6 is 79°
The measure of ∠7 is 79°
The measure of ∠8 is 79°
What are supplementary angles?
Supplementary angles is defined as angle of pair that angle measures whose sum is 180 degrees.
Angles ∠2 and ∠3 are supplementary angles
Given A || B
∠2 = 3x + 7 (Vertical opposite angles)
∠2 = ∠5 (Alternate Interior Angles)
So ∠5 = 3x + 7
4x + 5 + 3x + 7 = 180° (Both are supplementary Angles)
7x + 12 = 180°
7x = 168°
x = 24°
∠1 = ∠3 = 4(24) + 5 = 101°
∠2 = 3(24) + 7 = 79°
∠4 = ∠3 = 101°
∠5 = ∠6 = ∠2 = 79° (Vertical opposite angles)
5x - 29 = 5(24) - 19 = 101°
∠7 = ∠8 = 180° - 101° = 79°
The value of x is 24. The measures of angles ∠1,∠2,∠3,∠4,∠5,∠6,∠7,∠8 are 101°, 79°, 101°, 101°, 79°, 79°, 89°, 89° respectively.
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