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If edge A and angle C space complementary angles and B and D room supplementary angles, i beg your pardon of the following must it is in 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

95 degrees

Explanation:

If angle A is just one of the basic angles, then the other base angle have to measure 50 degrees. Since 50 + 50 + x = 180 means x = 80, the crest angle must measure 80 degrees.

You are watching: Each angle of a regular octagon has a measure of degrees.

If angle A is the peak angle, the two base angles should be equal. Because 50 + x + x = 180 method x = 65, the 2 base angles need to measure 65 degrees.

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

### Example inquiry #3 : exactly how To uncover An angle In A Polygon

In triangle ABC, the measure of edge A = 70 degrees, the measure up of angle Bx degrees, and the measure up of edge Cy degrees. What is the value of y in terms of x?

70 + x

110 – x

Explanation:

Since the 3 angles of a triangle sum to 180, we know that 70 + x + y = 180. Subtract 70 native both sides and also see that x + y = 110. Subtract x from both sides and see that y = 110 – x.

### Example question #4 : exactly how To uncover An angle In A Polygon

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

135

150

Explanation:

The sum of the inner angles, in degrees, that a regular polygon is offered by the formula 180(n – 2), wherein n is the number of sides. The problem comes to a polygon with twelve sides, therefore we will let n = 12. The amount of the internal angles in this polygon would be 180(12 – 2) = 180(10) = 1800.

Because the polygon is constant (meaning that is sides are all congruent), all of the angles have the same measure. Thus, if we division the sum of the procedures of the angles by the number of sides, we will have actually the measure up of each interior angle. In short, we need to divide 1800 through 12, which provides us 150.

The prize is 150.

### Example question #5 : exactly how To find An edge In A Polygon 45

Explanation:

Angle FHI is the supplement of edge FHG, i beg your pardon is an interior angle in the octagon. Once two angles are supplementary, their sum is equal to 180 degrees. If us can discover the measure of each interior angle in the octagon, then us can discover the supplement of edge FHG, i m sorry will give us the measure up of edge FHI.

The amount of the inner angles in a regular polygon is given by the formula 180(n – 2), where n is the number of sides in the polygon. An octagon has eight sides, therefore the sum of the angles of the octagon is 180(8 – 2) = 180(6) = 1080 degrees. Because the octagon is regular, all of its sides and also angles room congruent. Thus, the measure up of each angle is equal to the sum of that angles divided by 8. Therefore, each angle in the polygon has actually a measure of 1080/8 = 135 degrees. This means that angle FHG has actually a measure up of 135 degrees.

Now that we recognize the measure up of edge FHG, we can uncover the measure up of FHI. The amount of the actions of FHG and also FHI must be 180 degrees, due to the fact that the two angles kind a line and also are supplementary. We can write the adhering to equation:

Measure that FHG + measure up of FHI = 180

135 + measure of FHI = 180

Subtract 135 native both sides.

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Measure of FHI = 45 degrees.

The price is 45.

### Example question #6 : how To find An angle In A Polygon

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