In the triangles below, AB = QR BC = RP CA = PQ

Compute ∠C and ∆ABC and all angles of ∆PQR.

We know sum of all interior angles of a triangle is 180⁰.

In ∆ABC,

∠a + ∠b + ∠c = 180⁰

40⁰ + 60⁰ + ∠c = 180⁰

100⁰ + ∠c = 180⁰

∠c = 180⁰-100⁰

∠c = 80⁰

To find all angles in ∆PQR:

Given, AB = QR

BC = RP

CA = PQ

To find pairs of matching angles, the angles between any two of the corresponding sides in the two figures are matching angles.

Thus,

∠CAB = ∠PQR = 40⁰

∠ABC = ∠QRP = 60⁰

∠BCA = ∠RPQ = 80⁰