Question

In the triangle below, ab=qr, bc=pq,ca=rp. Compute the remaining angles of both triangles.​

Answer 1

Answer:

50°

Step-by-step explanation:

Given, AB = QR

BC = PQ

CA = RP, which are corresponding sides of both triangles.

Thus, angles between any two of the corresponding sides in the two figures are matching angles.

Finding matching angles will help us to compute the remaining angles.

Therefore,

∠ABC = ∠PQR = 70⁰

∠PRQ = ∠CAB = 60⁰

Now we have,

In ∆ABC,

∠a + ∠b + ∠c = 180⁰

60⁰ + 70⁰ + ∠c = 180⁰

130⁰ + ∠c = 180⁰

∠c = 180⁰-130⁰

∠c = 50⁰

In ∆PQR,

∠p + ∠q + ∠r = 180⁰

∠p + 70⁰ + 60⁰ = 180

∠p + 130⁰ = 180⁰

∠p = 180⁰-130⁰

∠p = 50⁰

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