Question

Please help me answer these 3 questions.

Answer 1

Answer:

If it helps mark me as brainliest

Step-by-step explanation:

(i) Angle DEB= 180°-126°= 54°

They are corresponding angles.

(ii)Angle DEC= Angle( DEB +BEC)=(54+90)°= 144°

(iii)126°-Angle BEC= 126°- 90°= 36°

Exterior angle property.

Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

line n is parallel to line m and they are crossed by transversals r and s.

Further, given that r and s are perpendicular to each other and m ∠ABE = 126°.

$\red{\large\underline{\sf{Solution-a}}}$

As it is given that m || n and s is transversal.

We know, sum of co - interior angles are supplementary.

So, m ∠ABE + m ∠DEB = 180°

126° + m ∠DEB = 180°

m ∠DEB = 180° - 126°

$\rm\implies \:\boxed{\tt{ m \angle \: DEB \: = \: 54 \degree \: }}$

$\green{\large\underline{\sf{Solution-b}}}$

Now, as it is given that r and s are perpendicular to each other.

So, m ∠BEC = 90°

Now, m ∠DEC = m ∠DEB + m ∠BEC = 54° + 90° = 144°

$\rm\implies \:\boxed{\tt{ m \angle \: DEC \: = \: 144 \degree \: }}$

$\purple{\large\underline{\sf{Solution-c}}}$

Now, In triangle BEC

∠ABE is exterior angle of triangle BEC.

We know, Exterior angle of a triangle is equals to sum of interior opposite angles.

So,

m ∠ABE = m ∠BEC + m ∠BCE

126° = 90° + m ∠BCE

m ∠BCE = 126° - 90°

$\rm\implies \:\boxed{\tt{ m \: \angle \: BCE \: = \: 36 \degree \: }}$

Hence,

$\boxed{\tt{ m \angle \: DEB \: = \: 54 \degree \: }}$

$\boxed{\tt{ m \angle \: DEC \: = \: 144 \degree \: }}$

$\boxed{\tt{ m \: \angle \: BCE \: = \: 36 \degree \: }}$

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ADDITIONAL INFORMATION

Parallel lines :- If the perpendicular distance between two lines are same throughout, such lines are called parallel lines.

If a line intersects two parallel lines at distinct points, such line is called transversal.

If two parallel lines are cut by a transversal, each pair of alternate interior angles are equal.

If two parallel lines are cut by a transversal, each pair of corresponding angles are equal.

If two parallel lines are cut by a transversal, each pair of interior angles on the same side of transversal are supplementary.