Question

If triangle ABC and triangle PQR are similar triangles such that angle A=31 and R =69, the angle Q is:
a) 70
b)100
c)90
d)80

Answer 1

Answer:

total sum of angles of triangle is 180. so, when we add A+R+P =180

so, 31 + 69 + x (because Q value is not given so we put x there as the substitute)=180 ans .. Q=80

Step-by-step explanation:

31+69+x =180

100+x=180

x = 180-100

x=80

Answer 2

∠Q =  80° if ΔABC ~ ΔPQR and ∠A  = 31° and ∠R = 69°

Given:

• ΔABC ~ ΔPQR
• ∠A=31°
• ∠R=69°

To Find:

• ∠Q

Solution:

Concept to used:

Corresponding angles of similar triangles are equal

Sum of angles of a triangle is 180°

Step 1:

As ΔABC ~ ΔPQR

∠P = ∠A  = 31°

Step 2:

Sum of angles of  ΔPQR = 180° and substitute  ∠P = 31° , ∠R = 69° and solve for ∠Q.

∠P + ∠Q + ∠R   = 180°

=> 31° + ∠Q + 69° = 180°

=> ∠Q + 100° = 180°

=> ∠Q =  180° - 100°

=> ∠Q =  80°

Correct option is (d) 80°

∠Q =  80° if ΔABC ~ ΔPQR and ∠A  = 31° and ∠R = 69°

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