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2 years ago

Hi please help !!! With steps as well please!

Mathematics

1 answer:

Scrat [10]2 years ago

7 0

Answer:

a) m = 60°, n = 30°

b) m = 20°, n = 45°

Step-by-step explanation:

The top and bottom horizontal lines are parallel, so angle m is an alternate interior angle congruent to the interior angle(s) of the equilateral triangle. Those angles are all 60°.

Angle n is the complement of angle m, so is 90°-60° = 30°

m = 60°, n = 30°

The base angles of the isosceles right triangle are n = 45°. (This should be a memorized fact. It is computed as (180° -90°)/2 = 45°.)

The base angles of the isosceles acute triangle are (180°-50°)/2 = 65°. Angle m is the difference between one of these and angle n.

m = 65° -45° = 20°

m = 20°, n = 45°

_____

Additional comment

The sum of angles of a triangle is 180°. The "base" angles of an isosceles triangle (one with two equal sides) are equal. If 'a' is the third angle, and 'b' are the base angles, you have ...

a + 2b = 180°

2b = 180° -a

b = (180° -a)/2 . . . . . . the relation used above

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