Question

Work out the value of angle x

Answer 1

well, it's isosceles so use base angles theorem

the top angle is also x

90 + 2x = 180

subtract 90 from both sides

2x = 90

divide both sides by 2

x = 45 degrees

Answer 2

x = 45 degrees

Explanation:

from the picture, we can see that the triangle is:

1) a right triangle (i.e one of the angles is 90 degrees)

and

2) An isosceles triangle (i.e two side lengths are equal)

Recall that for an isosceles triangle, the base angles (i.e the angles that are not 90 degrees) are identical.

In our case, we are given one of the base angles as x. By the above reasoning, the other missing base angle must also be x. Hence the three internal angles of the given triangle are 90 deg, x deg and x deg.

Also recall that the sum of the internal angles of a triangle must add up to 180 deg, hence,

90 + x + x = 180 deg (solve for x)

90 + 2x = 180

2x = 180 - 90

2x = 90

x = 90 / 2

x = 45 deg