Question

Determine the value of each unknown angles.

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Answer 1

d) x = 60

e) m = 60

g) q = 75

h) m = 75

Explanation:

d) This image is that of an equilateral triangle, or a triangle whose sides are all equal (also known as a regular triangle). One property of an equilateral triangle is that all of its angles are also equal. Because the angles of a triangle add up to 180° (Triangle Sum Theorem), each angle would be 180/3°, or 60°, so x = 60.

e) This problem shows two complementary angles. Complementary angles are two angles that add up to 90°. Because one of the angles is given, you can find the other by subtracting the given one from 90°:

m = 90 - 30

m = 60

g) This is an image of a triangle with two given angles and the missing one is the third angle, q. You can solve for q using the Triangle Sum Theorem, which states that the three interior angles of a triangle add to 180°:

50 + 55 + q = 180

105 + q = 180

q = 75

h) This image shows two parallel lines cut by a transversal. You can find m using the Corresponding Angles Theorem, which states that if parallel lines are cut by a transversal, the corresponding angles will be congruent. Because the lines are parallel, you know that m = 75 since the 75° angle is its corresponding angle.

Answer 2

For D:

A triangle always has 180 degrees total. No more, no less. Seeing as though all the sides and angles are the same length, we can just divide 180 by 3, giving us 60. x = 60 degrees.

For E:

We can see there is a 90 degree symbol that surmises both angles. We know the lower angle is 30 degrees, so m must equal 60 degrees.

For G:

Same concept as D, except we gotta do a bit of math. A triangle always has 180 degrees, So we add 50 and 55 together and get 105. Subtract 105 from 180 and we get 75. Therefore, your angle is 75 degrees.

For H:

The 75 degree angle and m are parallel, with the same line passing through it, meaning that m is identical to the other angle. m = 75.