In ΔCDE, \text{m}\angle C = (4x-16)^{\circ}m∠C=(4x−16) ∘ , \text{m}\angle D = (6x-1)^{\circ}m∠D=(6x−1) ∘ , and \text{m}\angle E
= (4x-13)^{\circ}m∠E=(4x−13) ∘ . Find \text{m}\angle C.M∠C.
1 answer:
Answer:
m∠C = 44°
Step-by-step explanation:
In ΔCDE,
m∠C=(4x−16) ∘
m∠D=(6x−1) ∘
m∠E=(4x−13) ∘ .
The sum of angles in a triangle = 180°
Step 1
We solve for x
m∠C + m∠D + m∠E
(4x−16)° + (6x−1)° + (4x−13)° = 180°
4x - 16 + 6x - 1 + 4x - 13 = 180°
4x + 6x + 4x -16 - 1 - 13 = 180°
14x - 30 = 180°
14x = 180+ 30
14x = 210
x = 210/14
x = 15
Step 2
Find m∠C
m∠C = (4x−16)°
m∠C = (4 × 15 - 16)°
m∠C = (60 - 16)°
m∠C = 44°
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