∠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:
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.
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