Question

Consider

In square ABCD, the diagonals intersect at G.
If mLAGD = a + 2b and mzABC = 2a - b, find the values of
a and b.
C

Answer 1

a = 54

b = 18

Explanation:

ABCD is a square. It's diagonals AC and BD intersects at G.

Since, diagonals of a square bisects at right angles.

`\therefore m\angle AGD = 90\degree`

`\implies a + 2b = 90\degree`

`\therefore a = 90\degree - 2b.....(1)`

Since, measure of each angle of a square is right angle.

`\therefore m\angle ABC = 90\degree`

`\implies 2a-b = 90\degree.......(2)`

From equations (1) & (2)

2(90° - 2b) - b = 90°

180° - 4b - b = 90°

-5b = 90° - 180°

-5b = - 90°

b = - 90°/(-5)

b = 18

Plug b = 18 in equation (1)

a = 90° - 2*18

a = 90° - 36°

a = 54