Question

In the given figure AS is parallel to BT,angle 4=angle 5. SB bisects angle AST.Find the measure of angle 1

Answer 1

Figure was missing in this question.

Refer to the attached image.

Given: AS is parallel to BT, $\angle 4=\angle 5$ and SB bisects angle AST that is ($\angle 2=\angle 3$)

To find: The measure of $\angle 1$

Solution:

Since AS is parallel to BT,

therefore, $\angle 2=\angle 5$ (Alternate angles are equal)

Since, $\angle 2=\angle 3$

So, $\angle 2=\angle 3=\angle 5 =x (say)$

In triangle BST, angle RSB is an exterior angle.

By exterior angle property,

$\angle RSB=\angle SBT+\angle BTS$

$\angle 1+\angle 2=\angle 4+\angle 5$

$\angle 1+x=x+x$

$\angle 1+x=2x$

$\angle 1=x$

Since, angle 1, 2 and 3 forms a linear pair.

$\angle 1+\angle 2+\angle 3=180^{\circ}$

$x+x+x=180^{\circ}$

$3x=180^{\circ}$

$x=60^{\circ}$

So, the measure of $\angle 1$ is 60 degrees.

Answer 2

Answer:

Given: AS is parallel to BT, \angle 4=\angle 5∠4=∠5 and SB bisects angle AST that is (\angle 2=\angle 3∠2=∠3 )

To find: The measure of \angle 1∠1

Solution:

Since AS is parallel to BT,

therefore, \angle 2=\angle 5∠2=∠5 (Alternate angles are equal)

Since, \angle 2=\angle 3∠2=∠3

So, \angle 2=\angle 3=\angle 5 =x (say)∠2=∠3=∠5=x(say)

In triangle BST, angle RSB is an exterior angle.

By exterior angle property,

\angle RSB=\angle SBT+\angle BTS∠RSB=∠SBT+∠BTS

\angle 1+\angle 2=\angle 4+\angle 5∠1+∠2=∠4+∠5

\angle 1+x=x+x∠1+x=x+x

\angle 1+x=2x∠1+x=2x

\angle 1=x∠1=x

Since, angle 1, 2 and 3 forms a linear pair.

\angle 1+\angle 2+\angle 3=180^{\circ}∠1+∠2+∠3=180

∘

x+x+x=180^{\circ}x+x+x=180

∘

3x=180^{\circ}3x=180

∘

x=60^{\circ}x=60

∘

So, the measure of \angle 1∠1 is 60 degrees.

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