bearing in mind that the sum of all interior angles in a polygon is
180(n - 2) n = number of sides in the polygon
a DECAgon, DECA=10, has 10 sides, and thus the sum of all its interior angles is 180(10 - 8) = 1440.
Answer:
Step-by-step explanation:
3). m∠1 = 180° - 98° = 82°
m∠7 = 180° - ( 98° + 23° ) = 59°
m∠6 = 180° - ( 70° + 59° ) = 51°
m∠9 = m∠6 = 51°
m∠10 = 180° - 51° = 129°
m∠4 = 180° - ( 70° + 51° ) = 59°
m∠54 = 180° - (23° + 59° ) = 98°
4). m∠1 = m∠4 = m∠11 = m∠13 = 90° - 54° = 36°
m∠2 = m∠5 = 90°
m∠6 = m∠3 = m∠8 = m∠10 = 54°
m∠7 = m∠9 = 90° + 36° = 126°
m∠12 = m∠14 = 180° - 36° = 144°
The submarine woulf be at 550 feet below sea level.
Answer:
88 degree
Step-by-step explanation:
We assume the measure of MN is x degree.
As the measure of LP is 30 degree more than that of MN, so that the measure of LP is: x + 30 degree
In the circle, as 4 points M,N,P,L are on the circle, we have:
+) ∡MPN = 1/2 * (measure of ∡MPQMN) = x/2 = ∡MPQ
+) ∡LMP =1/2 * (measure of LP) = (x+30)/2 = ∡QMP
We have ∡NQM and ∡MQP are complementary angles, so that:
∡MQP + ∡NQM = 180
=> ∡MQP = 180 - ∡NQM = 180 -103 = 77
In the triangle QMP, total measure of 3 internal angles are 180 degree, so that:
∡MQP + ∡QMP + ∡MPQ = 180
=> 77 + (x + 30)/2 + x/2 = 180
=> 77 + x/2 + 15 + x/2 = 180
=> x = 180 -77-15= 88
So that the measure of MN is 88 degree
