A, B & C lie on a straight line. D, C & E lie on a different straight line. Angle y = 96° and angle z = 52°. Work out x
2 answers
Question:
A, B & C lie on a straight line.
D, C & E lie on a different straight line.
Angle
y
= 96° and angle
z
= 52°.
Work out
x
D, C & E lie on a different straight line.
Angle
y
= 96° and angle
z
= 52°.
Work out
x
Answers
Answer:x = 136°Step-by-step explanation:We can use a theorem to help us.Theorem: The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.For exterior angle x, the remote interior angles are z and <CBD.From the theorem, we get this equation.x = z + m<CBDWe 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<CBDx = 52° + 84°x = 136°
Answer:x = 136°Step-by-step explanation:∠ABD = y = 96°, ∠ABD + ∠DBC must be equal to 180° because they form a straight angle.[tex]y + B = 180\\96 + B = 180\\B = 180 - 96 = 84[/tex] ∠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°. [tex]180=(180 - y) + 52 + C\\180=(180 - 96) + 52 + C\\180 - (52 + 84) = C\\C = 44[/tex]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°.[tex]180 = C + x\\180 = 44 + x\\x = 180-44\\x = 136\\[/tex]Angle ∠BCE = x = 136.
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