In parallelogram FIST, the measure of ∠OST is ____.

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Detailed Solution

In parallelogram FIST, the measure of ∠OST is

.
Given

∠ F I S = 60 °

.
As the opposite angles of a parallelogram are equal,
Then

∠ F T S = ∠ F I S = 60 °

.
Since,

F T ∥ I S

and TI is a transversal then the alternate angles are equal.

∠ F T O = ∠ S I O = 25 °

∴ ∠ S T O = ∠ F T S − ∠ F T O = 60 ° − 25 ° = 35 °

Now, we know the sum of linear angles

180 ∘

. So,

∠ F O T + ∠ S O T = 180 ° ⇒ 110 ° + ∠ S O T = 180 ° ⇒ ∠ S O T = 180 ° − 110 ° = 70 °

Δ T O S

the sum of all interior angles in a triangle is

180 °

∠ T S O + ∠ O T S + ∠ T O S = 180 ° ⇒ ∠ O T S = 180 ° − ∠ T S O − ∠ T O S ⇒ ∠ O T S = 180 ° − 70 ° − 35 ° ⇒ ∠ O T S = 75 °

Hence, the measure of

∠ O T S = 75 °

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