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3 years ago

Is this right ? Geometry

Mathematics

2 answers:

elixir [45]3 years ago

7 0

No, 12 is the wrong answer. 5 is correct

This is because since a and c are congruent that means y=52. And we already know that every triangle adds up to 180 degrees so, you add A and C and get 104 (52+52).
And 180-104=76 so, 14x+6 must =76.
14(5)=70+6=76. 76+104=180, therefore, x=5.

pogonyaev3 years ago

5 0

Answer: 5

Step-by-step explanation:

BA ≅ BC ⇒ ∠A ≅ ∠C

52 = y

The sum of the angles of a triangle equals 180°

∠A + ∠B + ∠C = 180

52 + 14x + 6 + 52 = 180

14x + 110 = 180

14x = 70

x = 5

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Answer:

See Below.

Step-by-step explanation:

In the given figure, AP = BP = PC.

And we want to prove that ∠ABC is a right angle.

Since AP = BP and BP = PC, we can create two isosceles triangles: ΔAPB and ΔCPB.

By the definition of isosceles triangles, in ΔAPB, ∠PAB and ∠PBA are equivalent. Let the measure of each of them be x°.

Likewise, in ΔCPB, ∠PCB and ∠PBC are equivalent.

And since AP = BP = PC, each of the angles∠PCB and ∠PBC will also be equivalent to x°.

And since the sum of the interior angles of a triangle total 180°, we acquire:

$\angle PAB+\angle PBA+\angle PCB+\angle PBC=180$

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$4x=180$

Hence:

$x=45^\circ$

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$\angle ABC=\angle PBA+\angle PBC=45+45=90^\circ$

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