Question

Work must be shown for this problem! The figure shown below is a rectangle. Give the angle value (numerical, not the letters).

Answer 1

58°

Explanation:

to find m∠CEB

triangle CEB is formed by the two parts of rectangle diagonals (and BC), and as we know, diagonals bisect each other, thus EB is congruent to EC, and it is an isosceles triangle

We also know that angles opposite congruent sides are congruent, thus,

angles EBC and ECB are congruent

thus angle ECB= 61°

We know that the inner angle measures of a triangle according to Angle Sum Theorem add up to 180°

Thus,m angle EBC + m angle ECB + m angle CEB= 180

Now we know that both EBC and ECB are angles with the measure of 61 °, so lets put the measures in instead of angles into the equation

61+61+m angle CEB=180

122 + m angle CEB =180

m angle CEB=180-122

m angle CEB=58°

Answer 2

58 degrees

Explanation:

In a rectangle, the two diagonals form four isosceles triangles. This means triangle EBC is isosceles. In an isosceles triangle, the two base angles are the same. So, angles EBC and BCE are both 61. Now, in a triangle, the three angles add up to 180. So, 61+61=122, and to find angle CEB you need to subtract 180-122. 180-122=58 degrees.