2 answers:
Answer:
m∠ABC = 68°
m∠DEF = 112°
Step-by-step explanation:
Supplementary angles are angles that add up to 180 degrees (they form a straight line).
If ∠ABC and ∠DEF are supplementary, that means that they add up to 180. We can write this in an equation:
- (6x + 8) + (12x - 8) = 180
Combine like terms.
Divide both sides by 18.
Find the measure of each angle by substituting 10 for x into both expressions for the angles.
m∠ABC = (6x + 8)°
m∠DEF = (12x - 8)°
<h2><u>Answer</u><u> </u><u>:</u></h2>
→ (6x + 8) + (12x - 8) = 180°
→ 6x + 8 + 12x - 8 = 180°
→ 18x = 180°
→ x = 180 ÷ 18
→ x = 10°
<u>Now, we are given that m∠ABC = (6x+8) just subsitute the value of x in it .</u>
→ m∠ABC = (6x + 8)
→ m∠ABC = (6 × 10 + 8)
→ m∠ABC = 60 + 8
→ m∠ABC = 68°
<u>Similarly, subsitute the value of x in m∠DEF = (12x - 8)°</u><u> </u><u>we</u><u> </u><u>get</u><u> </u><u>:</u>
→ m∠DEF = (12x - 8)°
→ m∠DEF = (12 × 10 - 8)
→ m∠DEF = 120 - 8
→ m∠DEF = 112°
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