Let ABC be an isosceles triangle with AB = AC and ∠BAC=30°. Side AB and the median AD contain points Q and P respectively (point
s P and Q are not at point A) in such a way that PC=PQ. Find m∠PQC.
1 answer:
Answer:
15°
Step-by-step explanation:
Since P is on the median of ΔABC, it is equidistant from points B and C as well as from C and Q. Thus, points B, C, and Q all lie on a circle centered at P. (See the attached diagram.)
The base angles (B and C) of triangle ABC are (180° -30°)/2 = 75°. This means arc QC of the circle centered at P has measure 150°. The diameter of circle P that includes point Q is defined to intersect circle P at R.
Central angle RPC is the difference between arcs QR and QC, so is 180° -150° = 30°. Inscribed angle RQC has half that measure, so is 15°. Angle PQC has the same measure as angle RQC, so is 15°.
Angle PQC is 15°.
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Answer:
The degree of a polynomial refers to the highest degree of its individual terms having non-zero coefficients.
Step-by-step explanation:
The degree of a polynomial refers to the highest degree of its individual terms having non-zero coefficients. For example;
A quadratic polynomial is a polynomial of degree 2. This polynomial takes the general form;
where a, b, and c are constants. This is usually referred to as a quadratic polynomial in x since x is the variable. The highest power of x in the polynomial is 2, hence the degree of any quadratic polynomial is 2.
A second example, consider the cubic polynomial;
The degree of this polynomial is 3.