Answer:
82°
Step-by-step explanation:
In a triangle, the interior angles sum to 180°.
Given that the three angles of a triangle are x°, (x + 10)° and (2x - 6)°, we can set the sum of these angles equal to 180° and solve for x:
[tex]\begin{aligned}x^{\circ}+(x+10)^{\circ}+(2x-6)^{\circ}&=180^{\circ}\\x+x+10+2x-6&=180\\4x+4&=180\\4x&=176\\x&=44\end{aligned}[/tex]
Now, substitute the found value of x into the three angle expressions:
[tex]x^{\circ}=44^{\circ}[/tex]
[tex](x+10)^{\circ}=(44+10)^{\circ}=54^{\circ}[/tex]
[tex](2x-6)^{\circ}=(2(44)-6)^{\circ}=82^{\circ}[/tex]
Therefore, the three angles of the triangle measure 44°, 54° and 82°.
So, the measure of the largest angle in the triangle is:
[tex]\huge\boxed{\boxed{82^{\circ}}}[/tex]
Answer:
[tex]82^\circ[/tex]
Step-by-step explanation:
In a triangle, the sum of all interior angles is always 180 degrees. Therefore, for any triangle, the sum of its three angles [tex]A[/tex], [tex]B[/tex], and [tex]C[/tex] is given by [tex]A + B + C = 180^\circ[/tex].
Let's denote the three angles in your triangle as [tex]x[/tex], [tex]x + 10[/tex], and [tex]2x - 6[/tex].
So, we have the equation:
[tex] x + (x + 10) + (2x - 6) = 180^\circ [/tex]
Now, combine like terms:
[tex] x+x+2x +10 -6 = 180 [/tex]
[tex] 4x + 4 = 180 [/tex]
Subtract 4 from both sides:
[tex] 4x + 4-4 = 180-4 [/tex]
[tex] 4x = 176 [/tex]
Divide both sides by 4:
[tex] x =\dfrac{176}{4}[/tex]
[tex] x = 44 [/tex]
Now that we know [tex]x[/tex], we can find the measure of each angle:
1. [tex]x = 44^\circ[/tex]
2. [tex]x + 10 =44+10= 54^\circ[/tex]
3. [tex]2x - 6 = 2\cdot 44 - 6 = 88-6 = 82^\circ[/tex]
Now, to find the measure of the largest angle, we look for the largest of these three values, which is [tex]82^\circ[/tex].
So, the measure of the largest angle in the triangle is:
[tex] \Large\boxed{\boxed{82^\circ}}[/tex]
