Angle 3 and angle 4 are adjacent, and angle 3 is 30 ° less than angle 4. Find angle 3 and angle 4.
March 13, 2021 | education
| By definition of adjacent angles, the sum of angles 3 and 4 is 180 °.
∠3 + ∠4 = 180. (1)
∠3 + 30 = ∠4. (2)
Let us subtract from equation (1) equation (2).
∠3 + ∠4 – ∠3 – 30 = 180 – ∠4.
∠4 – 30 = 180 – ∠4.
∠4 + ∠4 = 180 + 30.
2 * ∠4 = 210.
∠4 = 105 °.
From equation (1) we express ∠3:
∠3 = 180 – ∠4.
∠3 = 180 – 105 = 75.
Answer: ∠3 = 75 °, ∠4 = 105 °.
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