An isosceles triangle c a b is shown with angle a measuring 4 x minus 6, and angles c and b each measuring 3 x minus 2.

Question

Use the Triangle Angle Sum Theorem to find the measure of angle A
for the triangle in the diagram.

(1 point)
Responses

19°
19 degrees

55°
55 degrees

180°
180 degrees

70°

Answer 1

To find the measure of angle A in the given isosceles triangle (where angle A is at vertex A and is different from angles C and B), we can use the Triangle Angle Sum Theorem. This theorem states that the sum of the angles in a triangle is always 180 degrees.

We have:

• Angle \( A = 4x - 6 \)
• Angle \( B = 3x - 2 \)
• Angle \( C = 3x - 2 \)

Since angles B and C are equal (because it is an isosceles triangle), we can set up the equation as follows:

\[ A + B + C = 180 \]

Substituting for angles A, B, and C, we get:

\[ (4x - 6) + (3x - 2) + (3x - 2) = 180 \]

Combining like terms gives us:

\[ 4x - 6 + 3x - 2 + 3x - 2 = 180 \]

\[ (4x + 3x + 3x) + (-6 - 2 - 2) = 180 \]

\[ 10x - 10 = 180 \]

Now, add 10 to both sides:

\[ 10x = 190 \]

Now, divide by 10:

\[ x = 19 \]

Now that we have the value of \( x \), we can find angle A:

\[ A = 4x - 6 = 4(19) - 6 = 76 - 6 = 70 \]

Thus, the measure of angle A is \( \boxed{70°} \).