Question

asked Aug 13, 2021 216k views

1 Answer

AJ Venturella · Answer 1 · 2021-08-19T10:54:40+0000

Answer:

The measure of
$m \hat {BC}=34^0$

The measure of
$\angle DFE = 81^0$

Explanation:

The correct question is added in the diagram below.

From the diagram;

Given that:

∠A = 55°

∠P =38°

$m \hat {AC} = 86^0$

$m \hat{DE} = 2( \angle A )$

$m \hat{DE} = 2( 55^0 )$

$m \hat{DE} = 110^0$

a) it is clear and obvious that ∠P is formed at the exterior of the circle; so:

$m \angle P = \frac{m \hat {DE} -m \hat {BC} }{2}$

$38= \frac{110 -m \hat {BC} }{2}$

$38*2={110 -m \hat {BC} }{$

$76={110 -m \hat {BC} }{$

$m \hat {BC} }{={110 -76$

$m \hat {BC}=34^0$

b)
$m \hat {AC}=m \hat {AB}+ m \hat {BC}$

$86=m \hat {AB}+ 34$

$m \hat {AB}=86-34$

$m \hat {AB}=52$

∴
$\angle DFE = \frac{m \hat{DE}+m \hat{AB}}{2}$ (rule: chord intersecting inside the circle)

$\angle DFE = (110+52)/(2)$

$\angle DFE = (162)/(2)$

$\angle DFE = 81^0$

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