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Alja [10]
3 years ago
11

In the diagram, AD=CD=CB and measure of angle A=40°. How many degrees are in angle DCB?​

Mathematics
1 answer:
Ad libitum [116K]3 years ago
6 0

Answer:

20^{\circ}

Step-by-step explanation:

Consider triangle ACD. This triangle is isosceles triangle, because AD = DC. Angles adjacent to the base AC are congruent abgles, so

m\angle DAC=m\angle DCA=40^{\circ}

The sum of the measures of all interiror angles in the triangle is always 180^{\circ}, then

m\angle DAC+m\angle DCA+m\angle ADC=180^{\circ}\\ \\40^{\circ}+40^{\circ}+m\angle ADC=180^{\circ}\\ \\m\angle ADC=180^{\circ}-40^{\circ}-40^{\circ}=100^{\circ}

Angles ADC and BDC are supplementary angles (add up to 180^{\circ}), then

m\angle BDC=180^{\circ}-100^{\circ}=80^{\circ}

Consider triangle BCD. This triangle is isosceles triangle because BC = DC. Angles adjacent to the base BD are congruent abgles, so

m\angle BDC=m\angle DBC=80^{\circ}

The sum of the measures of all interiror angles in the triangle is always 180^{\circ}, then

m\angle DBC+m\angle BDC+m\angle BCD=180^{\circ}\\ \\80^{\circ}+80^{\circ}+m\angle BCD=180^{\circ}\\ \\m\angle BCD=180^{\circ}-80^{\circ}-80^{\circ}=20^{\circ}

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Step-by-step explanation:

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<u>Answer:</u>

(\frac{g}{f})(3)=\frac{-13}{21}\\

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Keywords: Domain, Operations on Functions

Learn more about functions at:

  • brainly.com/question/4767370
  • brainly.com/question/4770453

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