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4 years ago

Show that triangle MPT =Triangle MTP

Mathematics

1 answer:

exis [7]4 years ago

3 0

Unusual notation. I won't fuss with it.

a. We have isosceles PRT, so angle RPT = angle RTP.

By the definition of angle bisector, angle MTP = angle MTF, and angle MPT = angle MPU.

We have m angle RTP = m angle MTF + m angle MTP = 2 m angle MTP

Similarly, m angle RPT = 2 m angle MPT

2 m angle MTP = 2 m angle MPT

angle MPT = angle MPT

That's the first part.

b. That makes MPT isosceles.

c. 2x+124=180

2x = 56

x = 28 degrees

MTP = 28 degrees

d. We have angle RPT=angle RTP=56 so PRT=180-2(56)=68 degrees

PUT = 180 - UTP - UPT = 180 - 28 - 56 = 96 degrees

Bad drawing, PUT looks acute.

angle PRT = 68 degrees, angle PUT = 96 degrees

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Answer:

Year 2030.

Step-by-step explanation

In 1997, Let Tim's age = X years

In 1997, Let Sue's age = Y years

After 5 years in 2002, Tim's age = (X+ 5) years

After 5 years in 2002, Sue's age = (Y + 5) years

Now, According to question,

X + Y = 32 (sum of their ages) .......(1)

Y = 32 - X

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Substituting the value of Y in (2)

X + 5 = 2 (32 - X + 5)

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X = 69/3 = 23

Now ∵ Y = 32 - X and X = 23

∴ Y = 32 - 23 = 9

So, In 1997, Tim's age = 23 years and Sue's age = 9 years.

Let the year in which Sue's age will be three-fourth times of Tim's age be t.

Sue's age after t years = (9 + t) years.

Tim's age after t years = (23 + t) years

According to question,

$(9 + t) = \frac{3}{4} \times(23 + t)$

$4 (9 + t) = 3 (23 + t)$

$36 + 4t = 69 + 3t$

$4t - 3t = 69 - 36$

$t = 33$

The Year in which Sue's age will be three-fourth times of Tim's age is:

= (1997 + 33) = 2030.

4 0

4 years ago

Show that triangle MPT =Triangle MTP​

Show that triangle MPT =Triangle MTP