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,
[tex]\Delta BTS\cong \Delta GHD[/tex] (Given)
[tex]BS=GD[/tex] (CPCTC)
[tex]25=4x-11[/tex]
[tex]25+11=4x[/tex]
[tex]36=4x[/tex]
Divide both sides by 4.
[tex]9=x[/tex]
In ∆BTS,
[tex]\angle B+\angle T+\angle S=180^\circ[/tex] (Angle sum property)
[tex]21^\circ+\angle T+56^\circ=180^\circ[/tex]
[tex]77^\circ+\angle T=180^\circ[/tex]
[tex]\angle T=180^\circ-77^\circ[/tex]
[tex]\angle T=103^\circ[/tex]
Now,
[tex]\angle T=\angle H[/tex] (CPCTC)
[tex]103=7y+5[/tex]
[tex]103-5=7y[/tex]
[tex]98=7y[/tex]
Divide both sides by 7.
[tex]14=y[/tex]
Therefore, the value of x is 9 and value of y is 14.
