Question

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

Answer 1

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.