If angle A and also angle C space complementary angles and B and also D space supplementary angles, i beg your pardon of the following must be true?

In isosceles triangle *ABC*, the measure up of angle *A* is 50 degrees. Which is not a feasible measure for angle *B*?

65 degrees

**Correct answer:**

95 degrees

Explanation:

If angle *A* is just one of the base angles, climate the various other base angle have to measure 50 degrees. Because 50 + 50 + *x* = 180 method *x* = 80, the crest angle need to measure 80 degrees.

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If angle *A* is the crest angle, the two base angles have to be equal. Because 50 + *x* + *x* = 180 means *x* = 65, the 2 base angles should measure 65 degrees.

The only number provided that is not possible is 95 degrees.

### Example question #3 : how To discover An edge In A Polygon

In triangle *ABC*, the measure up of angle *A* = 70 degrees, the measure of angle *B* = *x* degrees, and the measure of angle *C* = *y* degrees. What is the value of *y* in state of *x*?

70 + *x*

**Correct answer:**

110 – *x*

Explanation:

Since the three angles the a triangle sum to 180, we know that 70 + *x* + *y* = 180. Subtract 70 from both sides and also see that *x* + *y* = 110. Subtract *x* indigenous both sides and see that *y* = 110 – *x*.

### Example inquiry #1 : just how To uncover An angle In A Polygon

What is the measure, in degrees, the each internal angle the a consistent convex polygon that has twelve sides?

135

**Correct answer:**

150

Explanation:

The amount of the internal angles, in degrees, of a continuous polygon is provided by the formula 180(*n –* 2), whereby *n* is the number of sides. The problem pertains to a polygon through twelve sides, for this reason we will let *n* = 12. The amount of the internal angles in this polygon would certainly be 180(12 – 2) = 180(10) = 1800.

Because the polygon is consistent (meaning that is sides are all congruent), every one of the angles have actually the exact same measure. Thus, if we division the amount of the steps of the angles by the variety of sides, we will have actually the measure up of each interior angle. In short, we must divide 1800 by 12, which offers us 150.

The answer is 150.

### Example inquiry #5 : exactly how To discover An angle In A Polygon

**Possible Answers:**

**Correct answer:**

45

Explanation:

Angle *FHI* is the supplement of edge *FHG*, i m sorry is an internal angle in the octagon. When two angles room supplementary, their amount is same to 180 degrees. If we can uncover the measure of each inner angle in the octagon, then we can uncover the supplement of angle *FHG*, i m sorry will provide us the measure of edge *FHI*.

The amount of the interior angles in a continual polygon is provided by the formula 180(*n –* 2), where *n* is the number of sides in the polygon. One octagon has eight sides, so the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, every one of its sides and also angles are congruent. Thus, the measure up of each angle is same to the sum of the angles separated by 8. Therefore, each angle in the polygon has actually a measure up of 1080/8 = 135 degrees. This way that edge *FHG* has actually a measure up of 135 degrees.

Now that we know the measure up of edge *FHG*, we can find the measure of *FHI*. The amount of the procedures of *FHG* and *FHI* need to be 180 degrees, because the 2 angles kind a line and also are supplementary. We have the right to write the complying with equation:

Measure of *FHG* + measure up of *FHI* = 180

135 + measure up of *FHI* = 180

Subtract 135 indigenous both sides.

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Measure of *FHI* = 45 degrees.

The price is 45.

### Example concern #6 : exactly how To uncover An edge In A Polygon

What is the measure up of each angle in a regular octagon?