Measure of ∠1 is 71° and measure of ∠2 is 109°
Step-by-step explanation:
Let us revise the meaning of linear pair angles
1. Linear pair angles are two adjacent angles formed when two lines
are intersecting
2. The measure of a straight angle is 180°, so a linear pair of angles
must add up to 180°
∵ ∠1 and ∠2 are linear pair angles
∴ m∠1 + m∠2 = 180°
∵ m∠1 = (6x + 11)°
∵ m∠2 = (10x + 9)°
- Substitute the values of the angles in the rule above
∴ (6x + 11)° + (10x + 9)° = 180°
- Add like terms in the left hand side
∴ (6x + 10x) + (11 + 9) = 180
∴ 16x + 20 = 180
- Subtract 20 from both sides
∴ 16x = 160
- Divide both sides by 16
∴ x = 10
Substitute the value of x by 10 in each measure
∵ m∠1 = (6x + 11)°
∴ m∠1 = 6(10) + 11 = 60 + 11
∴ m∠1 = 71°
∵ m∠2 = (10x + 9)°
∴ m∠2 = 10(10) + 9 = 100 + 9
∴ m∠2 = 109°
Measure of ∠1 is 71° and measure of ∠2 is 109°
Learn more:
You can learn more about angles in brainly.com/question/5312408
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