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lidiya [134]
3 years ago
10

If BTS=GHD BS=25 TS=14 BT=31 GD=4x-11 S=56 B=21 and H=(7y+5) find the values of x and y

Mathematics
1 answer:
77julia77 [94]3 years ago
3 0

Given:

Consider the completer question is "If ∆BTS≅∆GHD, BS=25, TS=14, BT=31, GD=4x-11, m∠S=56, m∠B=21 and m∠H=(7y+5), find the values of x and y.

To find:

The values of x and y.

Solution:

We have,

\Delta BTS\cong \Delta GHD       (Given)

BS=GD                       (CPCTC)

25=4x-11

25+11=4x

36=4x

Divide both sides by 4.

9=x

In ∆BTS,

\angle B+\angle T+\angle S=180^\circ    (Angle sum property)

21^\circ+\angle T+56^\circ=180^\circ

77^\circ+\angle T=180^\circ

\angle T=180^\circ-77^\circ

\angle T=103^\circ

Now,

\angle T=\angle H            (CPCTC)

103=7y+5

103-5=7y

98=7y

Divide both sides by 7.

14=y

Therefore, the value of x is 9 and value of y is 14.

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