Question

15. In the rhombus shown below, mz1 = 160°. What are the measures of 22 2 points

and 23 (YOU MUST FIND BOTH). *HINT: The interior angles of a triangle
have a sum of 180°. Opposite angles in a rhombus are congruent. An
isosceles triangle also has CONGRUENT base angles.
D

Answer 1

Answers:

angle2 = 160 degrees

angle3 = 10 degrees

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Step-by-step explanation:

The two triangles are congruent. We can prove this using SSS. The upper triangle is a mirrored copy of the lower triangle.

Since angle1 = 160 degrees, this means angle2 = 160 also. This is because the corresponding pieces of congruent triangles match up. Or you could use the second part of the hint which says "Opposite angles in a rhombus are congruent".

Let x be the measure of angle 3. For either isosceles triangle, it has congruent base angles measured x degrees. They add to the 160 degrees mentioned earlier to get a total of 180.

160+x+x = 180

2x+160 = 180

2x = 180-160

2x = 20

x = 20/2

x = 10

Angle 3 is 10 degrees.