Question

Solve for x
X
X=
75°

Answer 1

In triangle ABC with angle B denoted as x, angle C as 75 degrees, and AB equal to AC, solving for x yields
`\(x = 30^\circ\).`

In a triangle ABC where angle B is denoted as x and angle C is 75 degrees, and AB is equal to AC, we can use the fact that the sum of interior angles in a triangle is 180 degrees.

`\[ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ \]`

Substitute the given values:

`\[ \text{Angle A} + x + 75^\circ = 180^\circ \]`

To find angle A, subtract
`\(x + 75^\circ\)` from 180:

`\[ \text{Angle A} = 180^\circ - (x + 75^\circ) \]`

Since AB is equal to AC, angle A must be equal to angle C:

`\[ \text{Angle A} = 75^\circ \]`

Now set up the equation:

`\[ 75^\circ = 180^\circ - (x + 75^\circ) \]`

Solve for x:

`\[ x = 30^\circ \]`

So, in the triangle ABC, angle B is
`\(30^\circ\).`