A, B & C lie on a straight line.
2 answers:
Answer:
x = 136°
Step-by-step explanation:
∠ABD = y = 96°, ∠ABD + ∠DBC must be equal to 180° because they form a straight angle.
∠BDC = z = 52° and ∠DBC = B = 84.
Angles ∠BDC, ∠DBC, and ∠BCD must have a sum of 180° because the sum of the interior angles in a triangle is 180°.
The interior angle at C is 44. Line DCE forms a straight line, therefore having an angle of 180°. To find x, the sum of x and interior angle C is 180°.
Angle ∠BCE = x = 136.
Answer:
x = 136°
Step-by-step explanation:
We can use a theorem to help us.
<em>Theorem: </em>
<em>The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.</em>
For exterior angle x, the remote interior angles are z and <CBD.
From the theorem, we get this equation.
x = z + m<CBD
We know z = 52°.
We need to find m<CBD.
Angles CBD and y are a linear pair. They are supplementary, so the sum of their measures is 180°. We are given y = 96°.
m<CBD + y = 180°
m<CBD + 96° = 180°
m<CBD = 84°
x = z + m<CBD
x = 52° + 84°
x = 136°
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