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05.03.2020 •
Mathematics
Quadrilateral ERGF is inscribed in a circle Find the measure of angle E (Remember to show formulas equations and numbers in those formulasequations receive creditAlso, make sure to include units on your answer ) R - 2 + 6x G EK 7x - 13
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Ответ:
The measure of angle E is 75°.
Solution:
Given data:
∠E = 5x, ∠F = 7x – 13 and ∠R = –2 + 6x
A quadrilateral inscribed in a circle is called cyclic quadrilateral.
∠R and ∠G are opposite angles in a cyclic quadrilateral.
In cyclic quadrilateral, opposite angles are supplementary.
⇒ m∠R + m∠F = 180
⇒ –2 + 6x + 7x – 13 = 180
⇒ 13x – 15 = 180
Add 15 from both sides of the equation, we get
⇒ 13x = 195
Divide by 13 from both sides of the equation, we get
⇒ x = 15
To find the measure of angle E:
m∠E = 5x
m∠E = 5(15)
m∠E = 75
The measure of angle E is 75°.
Ответ:
2
Step-by-step explanation: