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3 years ago

One number is 9 more than another. if the sum of the two numbers is 163, find the two numbers.

Mathematics

1 answer:

tiny-mole [99]3 years ago

5 0

I think that one number is 77 and the other is 86. 77 + 9 is 86. 86 +77 is 163.

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Answer:

See Below.

Step-by-step explanation:

Statements: Reasons:

$\displaystyle 1)\text{ } \Delta APB \text{ and } \Delta AQC \text{ are equilateral triangles}$ Given

$\displaystyle 2) \text{ } m \angle PAB = 60$ Definition of equilateral.

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$\displaystyle 6)\text{ } m\angle QAB=m\angle QAC+m\angle BAC$ Angle Addition

$7)\text{ } m\angle QAB=m\angle PAB+m\angle BAC$ Substitution

$\displaystyle 8)\text{ } m\angle PAC=m\angle QAB$ Substitution

$9)\text{ } PA=BA$ Definition of equilateral

$10)\text{ } AC=AQ$ Definition of equilateral

$\displaystyle 11)\text{ } \Delta PAC \cong \Delta BAQ$ Side-Angle-Side Congruence*

$\displaystyle 12)\text{ } PC=BQ$ CPCTC

* SAS Congruence:

PA = BA

∠PAC = ∠QAB

AC = AQ

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One number is 9 more than another. if the sum of the two numbers is 163​, find the two numbers.

One number is 9 more than another. if the sum of the two numbers is 163, find the two numbers.