Question
You a triangle angle, some theorem to find the measure of angle a for the triangle in the diagram
Angle a equals 4X -6
Angle B equals 3X -2
Angle C equals 3X -2
Options
19°
180°
55°
70°
Angle a equals 4X -6
Angle B equals 3X -2
Angle C equals 3X -2
Options
19°
180°
55°
70°
Answers
Answered by
GPT-4o mini
To find the measure of angle \( a \) in the triangle, we can use the fact that the sum of the angles in a triangle is always \( 180^\circ \). Given the angles:
- Angle \( a = 4X - 6 \)
- Angle \( B = 3X - 2 \)
- Angle \( C = 3X - 2 \)
We can set up the equation:
\[
(4X - 6) + (3X - 2) + (3X - 2) = 180
\]
Now let's simplify:
\[
4X - 6 + 3X - 2 + 3X - 2 = 180
\]
Combine like terms:
\[
(4X + 3X + 3X) + (-6 - 2 - 2) = 180
\]
This simplifies to:
\[
10X - 10 = 180
\]
Now, solve for \( X \):
\[
10X = 180 + 10
\]
\[
10X = 190
\]
\[
X = 19
\]
Now that we have \( X \), we can find the measure of angle \( a \):
\[
a = 4X - 6
\]
\[
a = 4(19) - 6
\]
\[
a = 76 - 6
\]
\[
a = 70
\]
So the measure of angle \( a \) is \( 70^\circ \).
Therefore, the answer is:
**70°**
- Angle \( a = 4X - 6 \)
- Angle \( B = 3X - 2 \)
- Angle \( C = 3X - 2 \)
We can set up the equation:
\[
(4X - 6) + (3X - 2) + (3X - 2) = 180
\]
Now let's simplify:
\[
4X - 6 + 3X - 2 + 3X - 2 = 180
\]
Combine like terms:
\[
(4X + 3X + 3X) + (-6 - 2 - 2) = 180
\]
This simplifies to:
\[
10X - 10 = 180
\]
Now, solve for \( X \):
\[
10X = 180 + 10
\]
\[
10X = 190
\]
\[
X = 19
\]
Now that we have \( X \), we can find the measure of angle \( a \):
\[
a = 4X - 6
\]
\[
a = 4(19) - 6
\]
\[
a = 76 - 6
\]
\[
a = 70
\]
So the measure of angle \( a \) is \( 70^\circ \).
Therefore, the answer is:
**70°**
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