What is the measure of? angle PQR [Not drawn to scale) -51 -55 -74 -78
2 answers:
<u>Given</u>:
The exterior angle P is 74°
The measure of ∠PRQ is 51°
We need to determine the measure of ∠PQR
<u>Measure of ∠QPR:</u>
From the figure, it is obvious that P is the intersection of the two lines.
The angle 74° and ∠QPR are vertically opposite angles.
Since, vertically opposite angles are always equal, then the measure of ∠QPR is 74°
Thus, the measure of ∠QPR is 74°
<u>Measure of ∠PQR:</u>
The measure of ∠PQR can be determined using the triangle sum property.
Thus, we have;
Substituting the values, we get;
Thus, the measure of ∠PQR is 55°
Hence, Option B is the correct answer.
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Answer:
Using the Angle Addition Postulate, 20 + m∠DBC = 80. So, m∠DBC = 60° using the subtraction property of equality.
Step-by-step explanation:
If point D is the interior of angle ABC, then the angle addition postulate theory states that the sum of angle ABD and angle DBC is equals to angle ABC. The angle addition postulate is used to measure the resulting angle from two angles placed side by side.
From the attached image, ∠ABD and ∠DBC are placed side by side to form ∠ABC. Given that m∠ABD = 20° and m∠ABC = 80°
Hence, using angle addition postulate:
m∠ABD + m∠DBC = m∠ABC
20 + m∠DBC = 80
subtracting 20 from both sides (subtraction property of equality)
m∠DBC = 80 - 20
m∠DBC = 60°
