The value of ∠PQR is 70 degree.
<h3>What is a Circle ?</h3>
A circle is a round figure whose all points lie in the same plane.
It is given that
The figure shows a circle with points P, Q, and R on it forming an inscribed triangle, measure of arc QR is 100°,
The measure of an inscribed angle is equal to one-half of the measure of the arc subtended by it,
Therefore
m∠QPR = (1/2) * 100° = 50°.
Angles in triangle
∠ PRQ = 90°
and ∠QPR =20°.
The value of the angle ∠PQR is
By angle sum property
90 +20+ x = 180
110 +x = 180
x = 70
Therefore the value of ∠PQR is 70 degree.
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1. You can make use of the Pythagorean theorem considering "a" to be the longer leg of the largest right triangle. Then the value of "a" can be calculated from
(16+9)² = 15² +a²
625 -225 = a²
√400 = a = 20
2. You can find the altitude of the largest triangle (the length of the unmarked vertical line), then find "a" as the hypotenuse of the medium-sized right triangle.
That altitude is ...
√(15² -9²) = √144 = 12
so the length "a" is ...
a² = 12² +16² = 144 +256 = 400
a = √400 = 20
3. Based on the 15 and 9 dimensions of the smallest right triangle, you can realize that these triangles are multiples of the 3-4-5 right triangle. Then you can use relevant ratios of the side lengths of any of the triangles of which "a" is a part.
a = 4/3×15 = 4/5×(9+16) = 5/4×16 = 20
Angles LNM and MNI are supplementary, so their measures sum to 180°. This means
∡ LNM + ∡ MNI = 180°
∡ LNM = 180° - (19<em>x</em> + 2)°
The sum of the interior angles of any triangle is also 180°, so
∡ LNM + ∡ NML + ∡ MLN = 180°
(180° - (19<em>x</em> + 2))° + (15<em>x</em> - 2)° + (6<em>x</em>)° = 180°
Solve for <em>x</em> (I'll omit the degree symbol):
180 - 19<em>x</em> - 2 + 15<em>x</em> - 2 + 6<em>x</em> = 180
2<em>x</em> - 4 = 0
2<em>x</em> = 4
<em>x</em> = 2
Then ∡ MNI = (15•2 - 12)° = (30 - 12)° = 18°.
a=1 b= c=Step-by-step explanation:
Answer:
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Step-by-step explanation:
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4x+14
-M
X =
[?]7x7
4x+14
-M
X =
[?]7x7
4x+14
-M
X =
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4x+14
-M
X =
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