Question

If the length of PQ of ∆PRS is 9cm and G is centroid then PG=? and

GQ =?

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Answer 1

Step-by-step explanation:

Question 1:

In the given figure, ∠ACD is an exterior angle of ΔABC. ∠B = 40°, ∠A = 70°.

Find the measure of ∠ACD.

ANSWER:

In ΔABC,

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

= 70∘ + 40∘

= 110∘

Hence, the measure of ∠ACD is 110∘.

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Question 2:

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

ANSWER:

In ΔPQR,

∠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 ΔPQR 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∘respectively.

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Question 4:

The measure of one of the angles of a triangle is twice the measure of its smallest angle and the measure of the other is thrice the measure of the smallest angle. Find the measures of the three angles.

ANSWER:

Let us suppose the angles of a ΔPQR such that ∠P < ∠Q < ∠R.

A.T.Q,

∠Q = 2∠P

∠R = 2∠P

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

⇒ ∠P + 2∠P + 3∠P = 180∘

⇒ 6∠P = 180∘

⇒ ∠P = 30∘

Therefore,

∠P = 30∘

∠R = 60∘

∠R = 90∘

Hence, the measure of each angle is 30∘, 60∘ and 90∘respectively.