Question

If \triangle BTS\cong\triangle GHD△BTS≅△GHD, BS = 25, TS = 14, BT = 31, GD = 4x - 11, m\angle∠S = 56°, m\angle∠B = 21°, and m\angle∠H = (7y + 5)°, find the value of y.

Answer 1

Given:

△BTS≅△GHD, BS = 25, TS = 14, BT = 31, GD = 4x - 11, m∠S = 56°, m∠B = 21°, and m∠H = (7y + 5)°.

To find:

The value of y.

Solution:

In △BTS,

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

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

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

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

$m\angle T=103^\circ$

We have,

$\Delta BTS\cong \Delta GHD$

So, $\angle T\cong \angle H$             (By CPCTC)

Then, $m\angle T=m\angle H$

Now,

$103=7y+5$

$103-5=7y$

$98=7y$

Divide both sides by 7.

$14=y$

Therefore, the value of y is 14.