Question

observe the following figure and find angle P​

Answer 1

Answer:

∠P = 40°

Step-by-step explanation:

We have,

ΔABC and ΔPQR,

∠A = 80°,

∠B = 60°,

AB = 3.8 units, BC = 6 units, AC = 3√3 units

PR = 6√3 units, PQ = 12 units, RQ = 7.6 units.

Now,

In ΔABC,

∠A + ∠B + ∠C = 180° [Angle Sum Property]

80° + 60° + ∠C = 180°

140° + ∠C = 180°

∠C = 180° - 140°

∴ ∠C = 40°

Now,

If we can prove that ΔABC and ΔPQR are similar then we can say that their angles will be equal.

Now,

AB/RQ = (3.8/7.6) = (1/2)

BC/PQ = (6/12) = (1/2)

AC/PR = (3√3)/(6√3) = (1/2)

Hence,

(AB/RQ) = (BC/PQ) = (AC/PR)

[When the ratio of sides of two triangles are equal, they are similar.]

∴ ΔABC ~ ΔRQP (By S.S.S Similarity)

Then,

∠C = ∠P [Corresponding Parts of Similar Triangles]

We know that,

∠C = 40°

∴ ∠P = 40°

Hence,

∠P = 40°

Hope it helped and believing you understood it........All the best.

Answer 2

Answer:

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$by \: the \: triangle \: thales \: thearam \ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \\ \\ may \: be \: it \: will \: help \: you \: \\ \\ thanks}$

$by \: the \: formula \: of \: triangle \: thales \: thearom}$