Question

Find x for this triangle........

Answer 1

Let take the 37° angled traingle be 1st traingle and the other as second.

As the base angles of an isosceles traingle are equal so the left angle equals (of the 1st traingle)
180°-(37°+37°) [by angle sum property]
=180°- 74°
= 106°
Now in other traingle
Measure of one angle of it's base equals 180°-106° = 74°
As it is an isosceles traingle the other base angle would also be 74°

And the value of x =180° -(74°+74°) [by angle sum property]
= 180° - 148
= 32°

Answer 2

In ΔABO, ∠B = 37°
∵BO= AO
∴ΔABO is isosceles
∴∠BAO = ∠B = 37°

By ASP of Δ
∠BAO+∠B+∠AOB =180°
37°+37°+∠AOB= 180°
74°+∠AOB=180°
∴∠AOB= 106°

∠AOB + ∠AOC = 180° (straight angle)
106°+∠AOC=180°
∴∠AOC=74°

In ΔACO,
AC = CO
∴∠OAC =∠AOC = 74°

By ASP of Δ
∠OAC + ∠AOC + ∠ACO = 180°
2*74° + x = 180°
∴x= 32°