Question

In a triangle, ∠P - ∠Q = 40° and ∠P + ∠Q = 90°
∠P= ?
∠Q= ?
∠R= ?

Answer 1

Answer:

angle P =65°

angle Q=25°

angle R =90°

Step-by-step explanation:

adding

angle p - angle q + angle p + angle q =40+90

(+angle q and - angle q will be zero)

so . 2p = 130°

p = 130/2

so angle p = 65°

given

p - q = 40°

65 - q = 40°

65 - 40 = q

q = 25°

according to angle sum property of triangle

p + q + r =180°

90 + r = 180°

r = 90°

Answer 2

Answer:

In triangle PQR,

angle P - angle Q = 40° - (i) given

angle P + angle Q = 90° - (i) given

Adding (i) and (ii)

P - Q = 40°

P + Q = 90°

------------------

2P = 130°

:. P = 65°

Substitute P = 65° in (i)

P - Q = 40°

65 - Q = 40°

- Q = 40° - 65°

- Q = - 25°

:. Q = 25°

We know that, In triangle PQR,

angle P + angle Q + angle R = 180° - (Sum of measures of all angles in a triangle)

65° + 25° + R = 180°

90° + R = 180°

R = 180° - 90°

:. R = 90°

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