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Keith_Richards [23]

3 years ago

15

The ages of Alan, Beth, and Caleb Henley are consecutive integers with a sum of 48. Alan is the youngest, and Caleb is the oldes

t. Drag the phrases and expressions to complete the verbal statement and algebraic equation where a represents Alan's age.

1 answer:

Veseljchak [2.6K]3 years ago

3 0

Alan is 15. Beth is 16 and Caleb is 17

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Answer:

Part 7) Adjacent angles

m<SUR and m<RUN

m<TUP and m<PUQ

Part 8) Vertical acute angles

m<SUR and m<PUQ

m<RUN and m<TUP

Part 9) Supplementary angles

m<SUT and m<TUQ

m<SUR and m<QUR

Part 10) $m$

Part 11) m<RUQ is greater than m< TUR

Part 12) $x=21\°$

Part 13) $m$

Step-by-step explanation:

Part 7) we know that

we know that

Two angles are Adjacent when they have a common side and a common vertex

In this problem

m<SUR and m<RUN ----> are adjacent angles

because have a common side UR and a common vertex U

m<TUP and m<PUQ ----> are adjacent angles

because have a common side UP and a common vertex U

Part 8) we know that

An angle is acute when is measure is less than $90$ degrees

Vertical Angles are the pair of congruent angles opposite each other when two lines cross

In this problem

$m$ ------> by vertical angles

$m$ ------> by vertical angles

Part 9) we know that

Two angles are supplementary if its sum is equal to $180$ degrees

In this problem

$m$ ------> by supplementary angles

$m$ ------> by supplementary angles

Part 10) Find m<QUR

we know that

$m$ ------> by supplementary angles

we have

$m$

substitute

$41\°+m$

$m$

Part 11) which is greater m<TUR or m< RUQ

we know that

m<TUR=m<TUS+m<SUR

substitute the values

$m$

$m$ ----> see the procedure problem 10

therefore

m<RUQ is greater than m< TUR

Part 12) Find the measure angle x

$4x=84\°$ ------> by vertical angles

solve for x

$x=84\°/4=21\°$

Part 13) m<KMH

we know that

$m$ -----> by supplementary angles

$m$

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