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2 years ago

Help me pls due tmrw

Mathematics

1 answer:

stiv31 [10]2 years ago

8 0

( a )pairs of vertical angles :

AGB and EGD

Vertical angles are a pair of opposite angles formed by intersecting lines. Vertical angles are equal in magnitude.

( b ) a pair of adjacent angles :

AGB and BGC

Adjacent angles are two angles that have a common side and a common vertex (corner point) but do not overlap in any way.

AGB and BGD

Two angles are called supplementary when their measures add up to 180 degrees.

(d) A pair of complementary angles :

AGF and FGE

Two angles are called complementary when their measures add to 90 degrees.

(e) Find measure of CGD :

( look into the photo attached for better understanding)

CGD = 55°

<em>hope this helps :)</em>

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In a parallelogram ABCD point K belongs to diagonal BD so that BK:DK=1:4. If the extension of AK meets BC at point E, what is th

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Answer:

$\frac{BE}{EC} =\frac{1}{3}$

Step-by-step explanation:

In the diagram below we have

ABCD is a parallelogram. K is the point on diagonal BD, such that

$\frac{BK}{CK} =\frac{1}{4}$

And AK meets BC at E

now in Δ AKD and Δ BKE

∠AKD =∠BKE ( vertically opposite angles are equal)

since BC ║ AD and BD is transversal

∠ADK = ∠KBE ( alternate interior angles are equal )

By angle angle (AA) similarity theorem

Δ ADK and Δ EBK are similar

so we have

$\frac{AD}{BE} =\frac{DK}{BK}$

$\frac{AD}{BE} =\frac{4}{1}$

$\frac{BC}{BE}=\frac{4}{1}$ ( ABCD is parallelogram so AD=BC)

$\frac{BE+EC}{BE}=\frac{4}{1}$ ( BC= BE+EC)

$\frac{BE}{BE} +\frac{EC}{BE}=\frac{4}{1}$

$1+\frac{EC}{BE}=4$

$\frac{EC}{BE}=3$ ( subtracting 1 from both side )

$\frac{EC}{BE}=\frac{3}{1}$

taking reciprocal both side

$\frac{BE}{EC} =\frac{1}{3}$

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