Answer:
B: 30°, 78°, 72
Step-by-step explanation:
Given a [tex]\triangle ABC[/tex].
Let [tex]\angle A = x^\circ[/tex]
As per question statement, [tex]\angle B[/tex] is 18° more than twice of [tex]\angle A[/tex].
i.e
[tex]\angle B =(2x+18)^\circ[/tex]
[tex]\angle C[/tex] is 42° more than that of [tex]\angle A[/tex]
[tex]\angle C = (x+42)^\circ[/tex]
To find:
The angle measures of the triangle = ?
Solution:
We can use the angle sum property of a triangle here to find the three angles of the triangle.
As per angle sum property, the sum of all the three internal angles is equal to [tex]180^\circ[/tex].
[tex]\angle A + \angle B + \angle C= 180^\circ\\\Rightarrow x+2x+18+x+42=180^\circ\\\Rightarrow 4x+60=180\\\Rightarrow 4x=120\\\Rightarrow x= 30^\circ[/tex]
i.e. [tex]\angle A = 30^\circ[/tex]
[tex]\angle B = 2\times 30 + 18 = 78^\circ[/tex]
[tex]\angle C = 30+42 = 72^\circ[/tex]
Therefore, the correct answer is:
B: 30°, 78°, 72
