Answer:
<h3>140.3°</h3>
Step-by-step explanation:
Given the following angles
Interior angles are 110° and x°
Exterior angle = (4x+7)°
Using the triangular property which says that the sum of interior angle of a triangle is equal to its exterior angle, we have:
110 + x = 4x + 7
110 - 7 = 4x-x
103 = 3x
x = 103/3
x= 34.3°
Get the exterior angle
Exterior angle = 4x+7
Exterior angle = 4(34.3)+7
Exterior angle = 137.3+7
Exterior angle = 140.3°
<em>Hence the measure of the exterior angle shown is 140.3°</em>
-5x - 7 < 28.....add 7 to both sides
-5x < 35....divide both sides by -5, change the inequality sign (u change the inequality sign when dividing/multiplying by a negative number)
x > -7
Fiona and Pip win some money and share it in the ratio 6:1. Fiona gets £35 more than Pip. How much did they get altogether?
Let Pip get be x and fiona get be x+35
Ratio = 6:1
Answer:
148°
Step-by-step explanation:
The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.
arc QN = 2(74°) = 148°
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<em>Comment on the question and answer</em>
Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.
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We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.