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∠1 and ∠2 are linear pair. If m∠1 = 7x - 46 and m∠2 = 3x + 6. What is the measure of the smaller angle? Show your solution

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∠1 and ∠2 are linear pair. If m∠1 = 7x - 46 and m∠2 = 3x + 6.

What is the measure of the smaller angle?

⇒ The measure of the smaller angle is m∠2 =  72⁰.

To solve this problem, you can use the rule of angles on straight lines.

Straight Angle

If there are two angles that coincide with each other and form a straight angle, then one angle will be a complementary angle for the other angle. So the two angles can be called as complementary angles.

Rules for angles on a straight line:

  • ∠A + ∠B = 180⁰

Step-by-step explanation:

Given:

∠1 and ∠2 are linear pair.

If m∠1 = 7x - 46

m∠2 = 3x + 6

Question:

What is the measure of the smaller angle?

Solution:

Step 1

Find the value of x using the straight angle rule.

⇔ m∠1 + m∠2 = 180⁰

⇒ (7x - 46)⁰ + (3x + 6)⁰ = 180⁰

⇒ (7x + 3x)⁰ + (-46 + 6)⁰ = 180⁰

⇒ 10x - 40⁰ = 180⁰

⇒ 10x = 180⁰ + 40⁰

⇒ 10x = 220⁰

⇒ x = 220⁰ ÷ 10

⇒ x = 22⁰

Step 2

Determine ∠1 and ∠2.

⇔ m∠1 = (7x - 46)⁰

⇒ m∠1 = (7(22) - 46)⁰

⇒ m∠1 = (154 - 46)⁰

⇒ m∠1 = 108⁰

⇔ m∠2 = (3x + 6)⁰

⇒ m∠2 = (3(22) + 6)⁰

⇒ m∠2 = (66 + 6)⁰

⇒ m∠2 = 72⁰

So, the measure of the smaller angle is m∠2 =  72⁰.

Learn more about:

  • Which of the following is the if-then form of the statement?" < 1 and < 2 are complementary angles": https://brainly.ph/question/24674050

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