Answer:
x = 3 or x = -2
Step-by-step explanation:
Solve for x over the real numbers:
(x + 2) (x - 3) = 0
Hint: | Find the roots of each term in the product separately.
Split into two equations:
x - 3 = 0 or x + 2 = 0
Hint: | Look at the first equation: Solve for x.
Add 3 to both sides:
x = 3 or x + 2 = 0
Hint: | Look at the second equation: Solve for x.
Subtract 2 from both sides:
Answer: x = 3 or x = -2
Answer:
x = 10°
Step-by-step explanation:
a). Since, opposite angles of a cyclic quadrilateral are supplementary angles"
Therefore, in cyclic quadrilateral ABDE,
m∠ABD + m∠AED = 180°
110° + m∠AED = 180°
m∠AED = 180° - 110°
= 70°
b). AD = ED [Given]
m∠EAD = m∠AED [Since, opposite angles of equal sides are equal in measure]
m∠EAD = m∠AED = 70°
By triangle sum theorem in ΔABD,
m∠BAD + m∠ABD + m∠ADB = 180°
m∠BAD + 110° + 40° = 180°
m∠BAD = 180 - 150
= 30°
m∠AEB = m∠AED + m∠DAB [By angles addition postulate]
m∠AEB = 70° + 30°
= 100°
By triangle sum theorem in the large triangle,
x° + m∠AEB + m∠EAB = 180°
x° + 100° + 70° = 180°
x = 180 - 170
x = 10°
Answer:
m∠DEC = 78°
Step-by-step explanation:
Given information: AC = AD, AB⊥BD, m∠DAC = 44° and CE bisects ∠ACD.
If two sides of a triangles are congruent then the opposite angles of congruent sides are congruent.
AC = AD (Given)
According to the angle sum property, the sum of interior angles of a triangle is 180°.
Divide both sides by 2.
CE bisects ∠ACD.
Use angle sum property in triangle CDE,
Subtract 102 from both sides.
Therefore, the measure of angle DEC is 78°.
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