Question

What is the value of x with clear working out please?

Answer 1

Answer: x is 46°

Explanation:

• Let's first find Angle ACB

`{ \rm{ \angle ACB + 23 \degree + 90 \degree = 180 \degree}} \\ \\ { \rm{ \angle ACB = (180 - 90 - 23) \degree}} \\ \\ { \underline{ \rm{ \: \angle ACB = 67 \degree}}}`

• From alternative angles, x = Angle BAC.

• Since AB = AC, then Angle ABC = Angle ACB

`{ \rm{x + \angle ABC + \angle ACB = 180 \degree}} \\ \\ { \rm{x + 67 \degree + 67 \degree = 180 \degree}} \\ \\ { \rm{x + 134 \degree = 180 \degree}} \\ \\ { \boxed{ \rm{x = 46 \degree}}}`

Answer 2

let me add a bit more material, to the great reply above, which is absolutely correct.

we know that AB = AC, that means that triangle ABC is an isosceles and that its two angles at the "base" are congruent, namely the blue angles in the picture.

Since all flat-lines are 180°, then we know the angle to the left of point B is 180 - 44 - 23, and that angle is a corresponding angle with 67 + x.