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.
1 answer:
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 1
We find the variable x
The sum of angles in a triangle is 180°
Hence,
ΔVWX = m∠V + m∠W +m∠X
180° = (7x - 1)° + (4x + 16)° + (3x - 17)°
180° = 7x - 1 + 4x + 16 + 3x - 17
180° = 7x + 4x + 3x - 1 + 16 - 17
180° = 14x -2
Collect like terms
180° + 2 = 14x
182° = 14x
x = 182°/14
x = 13°
Step 2
We find m∠X
m∠X = (3x−17) ∘
x = 13
m∠X = (3 × 13 − 17)°
m∠X = (39 − 17)°
m∠X = 22°
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