Respuesta :
Question:
The measures of the angles of △ABC are given by the expressions in the table. Angle Measure
A (6x−1)°
B 20°
C (x + 14)°
What are the measures of angles A and C? Enter your answers in the boxes.
m∠A= º
m∠C= º
Answer:
The measures of the angles A and C are [tex]$\angle A=125^{\circ}$[/tex] and [tex]$\angle \mathrm{C}=35^{\circ}$[/tex]
Explanation:
The measures of angles of ΔABC are [tex]\angle A =(6x-1)^{\circ}[/tex] , [tex]\angle B=20^{\circ}[/tex] and [tex]\angle C=(x+14)^{\circ}[/tex]
By angle sum property, we have,
[tex]\angle A+ \angle B+ \angle C = 180^{\circ}[/tex]
[tex]6x-1+20+x+14=180[/tex]
[tex]7x+33=180[/tex]
[tex]7x=147[/tex]
[tex]x=21[/tex]
Thus, substituting [tex]x=21[/tex] in [tex]\angle A =(6x-1)^{\circ}[/tex] , we get,
[tex]\angle A =(6x-1)^{\circ}=(6(21)-1)^{\circ}[/tex]
[tex]\angle A = 126-1[/tex]
[tex]\angle A=125^{\circ}[/tex]
Also, substituting [tex]x=21[/tex] in [tex]\angle C=(x+14)^{\circ}[/tex] , we get,
[tex]\angle C=(x+14)^{\circ}=(21+14)^{\circ}[/tex]
[tex]$\angle \mathrm{C}=35^{\circ}$[/tex]
Hence, the value of A and C are [tex]$\angle A=125^{\circ}$[/tex] and [tex]$\angle \mathrm{C}=35^{\circ}$[/tex]
The measures of angles A and C is mathematically given as
mZA= 281/3
mZC = 178/3
What are the measures of angles A and C?
An Angle is a corner compressing of a projecting part .
Question Parameter(s):
Angle Measure
(6 - 1)
20°
(x + 14)
Generally, the equation for a triangle is mathematically given as
∠A + ∠B + ∠C = 180
(4x - 13)° + (15)° + (2x + 18)° = 180°
6x = 160
x = 26.67
In conclusion
mZA = ( 4x - 13 )
mZA= 281/3
mZC = ( 2x + 18 )
mZC = 178/3
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