In ΔVWX, \text{m}\angle V = (7x-1)^{\circ}m∠V=(7x−1) ∘ , \text{m}\angle W = (4x+16)^{\circ}m∠W=(4x+16) ∘ , and \text{m}\angle X = (3x-17)^{\circ}m∠X=(3x−17) ∘ . Find \text{m}\angle X.M∠X.
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Question:
In ΔVWX, \text{m}\angle V = (7x-1)^{\circ}m∠V=(7x−1) ∘ , \text{m}\angle W = (4x+16)^{\circ}m∠W=(4x+16) ∘ , and \text{m}\angle X = (3x-17)^{\circ}m∠X=(3x−17) ∘ . Find \text{m}\angle X.M∠X.
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Answer:m∠X= 22°Step-by-step explanation:In ΔVWX:m∠V=(7x−1) ∘ m∠W=(4x+16) ∘ ,m∠X=(3x−17) ∘ . Find M∠X.Step 1We find the variable xThe sum of angles in a triangle is 180°Hence, ΔVWX = m∠V + m∠W +m∠X180° = (7x - 1)° + (4x + 16)° + (3x - 17)°180° = 7x - 1 + 4x + 16 + 3x - 17180° = 7x + 4x + 3x - 1 + 16 - 17180° = 14x -2Collect like terms180° + 2 = 14x182° = 14xx = 182°/14x = 13°Step 2We find m∠Xm∠X = (3x−17) ∘x = 13m∠X = (3 × 13 − 17)°m∠X = (39 − 17)°m∠X = 22°
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