Question

guided interactive vocabulary match - up!
instruction: match the vocabulary word with the correct definition
linear
adjacent
side
vertical
obtuse
straight
supplementary
acute
vertex
complementary
1
2
3
4
5
6
7
8
9
10
11
12
this describes an angle
sharing a common
vertex and a common side.
this describes an angle
that has a measure
between 90
and 180 degrees.
this refers to a point,
line, or plane that
divides a geometric
figure into two congruent
parts.
this describes a pair of
angles that are non - adjacent
and whose sum is
180 degrees.
this refers to one of the
rays that form an angle.
this describes a pair of
angles with a common vertex
and common side whose
non - common sides are
opposite rays.
the common endpoint
of two rays that form
an angle.
this describes an angle
that has a measure
greater than 0 degrees
and less than 90
degrees.
these are also called
\opposite angles\. they
are non - adjacent angles
formed by the intersection
of two lines.
this describes a pair of
adjacent angles whose
non - common sides are
opposite rays.
this describes an angle
that has a measure
that measures exactly
180 degrees.
this describes a pair of
angles whose sum of the
measures that equal
90 degrees.
i do: example
find the m∠abc in the diagram below.
we do: example
find the m∠abd in the diagram below.
you do: check for understanding
if m∠pqr = 141°, find each
measure.
x=
m∠pqs=

Explanation:

Step1: Set up an equation

Since $\angle PQR=\angle PQS+\angle SQR$, we have $(13x + 4)+(10x-1)=141$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the left - hand side: $(13x+10x)+(4 - 1)=141$, which simplifies to $23x+3 = 141$.

Step3: Solve for $x$

Subtract 3 from both sides of the equation: $23x=141 - 3=138$. Then divide both sides by 23: $x=\frac{138}{23}=6$.

Step4: Find $\angle PQS$

Substitute $x = 6$ into the expression for $\angle PQS$. $\angle PQS=13x + 4=13\times6+4=78 + 4=82^{\circ}$.

Answer:

$x = 6$, $m\angle PQS=82^{\circ}$