Given: QS bisects ∠TQR; TQ ≅ RQ.

2 answers:

8 0

We know that segment QS bisects angle TQR because it is given. By the definition of angle bisector, angle TQS is congruent to angle RQS. We see that segment QS is congruent to segment SQ by the reflexive property. Therefore, we can conclude that triangles QRS and QTS are congruent by SAS.

krek1111 [17]2 years ago

7 0

It is given,
rqs,
the reflexive property,
sas

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In the diagram of circle o, what is the measure of ABC? 27° 54° 108° 120°

Vlad1618 [11]

Given:

Given that a circle O with two tangents BA and BC.

The major arc AC is 234°

The minor arc AC is 126°

We need to determine the measure of ∠ABC

Measure of ∠ABC:

We know the property that, "if a tangent and a secant, two tangents or two secants intersect in the interior of the circle, then the measure of angle formed is one half the difference of the measures of the intercepted arcs."

Hence, applying the above property, we have;

$\angle ABC=\frac{1}{2}( major \widehat{AC} - minor \widehat{AC})$

Substituting the values, we get;

$\angle ABC=\frac{1}{2}( 234^{\circ} -126^{\circ})$

$\angle ABC=\frac{1}{2}( 108^{\circ})$

$\angle ABC=54^{\circ}$

Thus, the measure of ∠ABC is 54°

Hence, Option b is the correct answer.

5 0

2 years ago

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pishuonlain [190]

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