Question

Chords AB and CD intersect each other at point E. Find m∠BEC, if the measures of arc AD is 54°, and BC is 70°.

Answer 1

Answer:

${\angle}BEC=62^{\circ}$

Step-by-step explanation:

Given:It is given that Chords AB and CD intersect each other at point E.

To find: The measure of ∠BEC.

Construction: Join AC.

Solution:

It is given that Chords AB and CD intersect each other at point E.

Now, we know that the inscribed angle is the half of the intercepted arc, thus

${\angle}ACD={\frac{1}{2}}(AD)$

${\angle}ACD={\frac{1}{2}}(54^{\circ})$

${\angle}ACD=27^{\circ}$

And, ${\angle}CAB={\frac{1}{2}}(CB)$

${\angle}CAB={\frac{1}{2}}(70^{\circ})$

${\angle}CAB=35^{\circ}$

Now, in ΔAEC, we have

${\angle}CAE+{\angle}ACE+{\angle}AEC=180^{\circ}$ (Angle sum property of triangles)

$35+27+{\angle}AEC=180$

${\angle}AEC=118^{\circ}$

Also, using the straight line property, we have

${\angle}AEC+{\angle}CEB=180^{\circ}$

$118+{\angle}CEB=180$

${\angle}CEB=62^{\circ}$

Therefore, the measure of ${\angle}BEC$ is $62^{\circ}$.

Answer 2

Answer:

62°

Step-by-step explanation:

consider the solution with short explanation (find it in the attachment).