Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C? Enter your answer in the box. ° A quadrilateral inscribed in a circle. The vertices of quadrilateral lie on the edge of the circle and are labeled as A, B, C, and D. The interior angle A is labeled as left parenthesis x plus 15 right parenthesis degrees. The angle B is labeled as left parenthesis x plus 10 right parenthesis degrees. The angle D is labeled as left parenthesis x plus 24 right parenthesis degrees.
Answers
Answered by
2
Answer:
Consider the property of cyclic quadrilaterals for which opposite angles are
supplementary, then:
m∠A + m∠C = 180∘
Since,
we are given that m∠A = (2x + 9)° and m∠C = (3x + 1)°,
we can substitute to find the value of x:
2x + 9 + 3x + 1 = 180
5x + 10 = 180
5x = 170
therefore x = 34
Now, we can substitute in the above value of x to find m∠A: m∠A = (2x + 9)° = (2 × 34 + 9)° = 77°
Therefore, the m∠A = 77°
Answered by
13
Answer:
92
Step-by-step explanation:
i just took the quiz
Similar questions
Social Sciences,
6 months ago
Social Sciences,
6 months ago
Environmental Sciences,
6 months ago
Geography,
1 year ago