Question

in given figure, angle Q : angle R = 2:3 . Find (I) angle Q (ii) angle R

Answer 1

angle Q = 130° same segment angle
angle R = sum of two angle = third Angle
so.......
angle is 25°

Answer 2

In triangle PQR,
ANGLE P + 130° = 180°
ANGLE P = 180° - 130°
ANGLE P = 50°

ANGLE P + ANGLE Q + ANGLE R =180°
50° + ANGLE Q + ANGLE R = 180°
ANGLE Q + ANGLE R = 180° - 50°
ANGLE Q + ANGLE R = 130°

Then,
ANGLE Q : ANGLE R = 2 : 3
ANGLE Q / ANGLE R = 2 / 3
ANGLE Q + ANGLE R / ANGLE R = 2+3/3____ (By Componendo)
130° / ANGLE R = 5 / 3
3 × 130° = 5 × ANGLE R
390° = 5 × ANGLE R
ANGLE R = 390° / 5
ANGLE R = 78°

ANGLE P + ANGLE Q + ANGLE R = 180°
50° + ANGLE Q + 78° = 180°
ANGLE Q + 128° = 180°
ANGLE Q = 180° - 128°
ANGLE Q = 52°

Hence, ANGLE P = 50°, ANGLE Q = 52°, ANGLE R = 78°

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