in the given figure ABCD is a cyclic quadrilateral side CD is produced on both sides such that BC b is equal to 110 degree and a d q is equal to 95 degree find the values of a and b
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Given,
Quad. ABCD is a cyclic quadrilateral.
in which,
∠BCP = 110°
∠ADQ = 95°
To find : m∠DAB and m∠CBA
Solution :
∠AQD +∠ADC = 180° ⇒ LINEAR PAIR
⇒ ∠ADC = (180 - 95)°
= 85 °
∠BCP+∠BCD = 180° ⇒ LINEAR PAIR
⇒ ∠BCD = (180 - 110)°
= 70 °
NOW,
∠DAB + ∠ BCD = 180° ⇔ (∵ In a cyclic quadrilateral opposite angles are supplementary.)
⇒ ∠DAB = (180 - 70)°
= 110°
∠CBA + ∠ ACD = 180° ⇔ (∵ In a cyclic quadrilateral opposite angles are supplementary.)
⇒ ∠CBA= (180 - 95)°
= 85°
∴ The measure of ∠DAB and ∠CBA is 110° and 80° respectively.
Answered by
0
Answer:
Step-by-step explanation:
Given,
Quadrilateral ABCD is a cyclic quadrilateral,
In which,
∠BCP=110°
∠ADQ=95°
We have to find, ∠DAB AND ∠CBA
Solution :
∠AQD +∠ADC = 180° ⇒ LINEAR PAIR
⇒ ∠ADC = (180 - 95)°
= 85 °
∠BCP+∠BCD = 180° ⇒ LINEAR PAIR
⇒ ∠BCD = (180 - 110)°
= 70 °
NOW,
∠DAB + ∠ BCD = 180° ⇔ (∵ In a cyclic quadrilateral opposite angles are supplementary.)
⇒ ∠DAB = (180 - 70)°
= 110°
∠CBA + ∠ ACD = 180° ⇔ (∵ In a cyclic quadrilateral opposite angles are supplementary.)
⇒ ∠CBA= (180 - 95)°
= 85°
∴ The measure of ∠DAB and ∠CBA is 110° and 80° respectively.
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