Question

Examine whether the △ABC can be constructed such that in △ ABC,
m∠ A= 85°, m∠B= 115° and AB= 5cm. Justify your answer.

Answer 1

Answer:

In ∆ABC,

∠ACD = ∠A + ∠B (Exterior angle property)

= 70∘ + 40∘

= 110∘

Hence, the measure of ∠ACD is 110∘.

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Question 2:

In ∆PQR, ∠P = 70°, ∠Q = 65 ° then find ∠R.

ANSWER:

In ∆PQR,

∠P + ∠Q + ∠R = 180∘ (Angle sum property)

⇒ 70∘ + 65∘ + ∠R = 180∘

⇒ 135∘ + ∠R = 180∘

⇒ ∠R = 180∘ − 135∘

= 45∘

Hence, the measure of ∠R is 45∘.

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Question 3:

The measures of angles of a triangle are x°, ( x-20)°, (x-40)°. Find the measure of each angle.

ANSWER:

Let us suppose the angles ∠P, ∠Q, ∠Rof a ∆PQR be x°, (x - 20)°, (x - 40)° respectively.

∠P + ∠Q + ∠R = 180∘ (Angle sum property)

⇒ x∘ + (x - 20)° + (x - 40)° = 180∘

⇒ 3x - 60 = 180

⇒ 3x = 240

⇒ x = 80

Therefore,

∠P = 80∘

∠R = (80 - 20)°

= 60∘

∠R = (80 - 40)°

= 40∘

Hence, the measure of each angle is 80∘, 60∘ and 40∘respectivel