Question

n and triangle pqr angle p is equal to 42 degree and angle R is equals to 55 degree what is the measure of angle QP​

Answer 1

Answer:

Given,

∠P−∠Q=42 (I)

∠Q−∠R=21 (II)

Sum of angles = 180

∠P+∠Q+∠R=180 (III)

Add all the three equations:

2∠P+∠Q=180+42+21

2∠P+∠Q=243 (IV)

Add I and IV,

2∠P+∠P=243+42

3∠P=285

∠P=95

∘

From IV, ∠Q=243−2×95

∠Q=53

∘

From II,

∠R=53−21=32

∘

Answer 2

Given,

∠P−∠Q=42 (I)

∠Q−∠R=21 (II)

Sum of angles = 180

∠P+∠Q+∠R=180 (III)

Add all the three equations:

2∠P+∠Q=180+42+21

2∠P+∠Q=243 (IV)

Add I and IV,

2∠P+∠P=243+42

3∠P=285

∠P=95 ∘

From IV,

∠Q=243−2×95

∠Q=53 ∘

From II,

∠R=53−21=32 ∘