△CDE∼△PQR. m∠C = 13°, m∠D = 65°. What are the measures of angles P, Q, and R?
Since ∆CDE ∼ ∆PQR, the corresponding angles of the triangles are equal. Therefore, m∠P = 13° and m∠Q = 65°. Since the sum of the angles in a triangle is 180°, we can calculate m∠R as follows:
m∠C + m∠D + m∠R = 180°
13° + 65° + m∠R = 180°
78° + m∠R = 180°
m∠R = 180° - 78°
m∠R = 102°
Therefore, the measures of angles P, Q, and R are m∠P = 13°, m∠Q = 65°, and m∠R = 102°.
△XYZ∼△RST. m∠X = 50°, m∠S = 79°. What is the measure of angle T?
Since ∆XYZ ∼ ∆RST, the corresponding angles of the triangles are equal. Therefore, m∠T = 50°.
Therefore, the measure of angle T is 50°.
Given △ABC∼△DEF, m∠A = 52°, and m∠E = 11°, what is the measure of angle C?
Since ∆ABC ∼ ∆DEF, the corresponding angles of the triangles are equal. Therefore, m∠C = m∠F.
m∠A + m∠B + m∠C = 180° (sum of angles in a triangle)
52° + m∠B + m∠C = 180°
m∠B + m∠C = 180° - 52°
m∠B + m∠C = 128°
m∠D + m∠E + m∠F = 180° (sum of angles in a triangle)
m∠D + 11° + m∠F = 180°
m∠D + m∠F = 180° - 11°
m∠D + m∠F = 169°
Since ∆ABC ∼ ∆DEF, we can set up a proportion:
m∠B + m∠C / m∠D + m∠F = BC / DE
(128°) / (169°) = BC / DE
Multiplying both sides by DE, we get:
BC = DE * (128° / 169°)
m∠C = m∠F = BC / DE * m∠D
Substituting the values we know, we get:
m∠C = DE * (128° / 169°) * (169°/128°)
m∠C = DE
Therefore, the measure of angle C is equal to the measure of angle E, which is 11°.
Given △PQR∼△LMN, m∠Q = 113°, and m∠R = 26°, what is the measure of angle N?
Since ∆PQR ∼ ∆LMN, the corresponding angles of the triangles are equal. Therefore, m∠N = m∠R.
Therefore, the measure of angle N is 26°.
Line AB is on the coordinate plane and does not pass through the origin. Line AB is dilated with a scale factor of 3 and a center of dilation at the origin to create line A′B′ . Describe the effect of the dilation on line AB . In particular, make sure to describe the relative location and size of line A′B′ compared to line AB . If Line AB was dilated with a scale factor of 1/3 , how would your answer change?
When line AB is dilated with a scale factor of 3 and a center of dilation at the origin, line A'B' will be three times longer than line AB. Additionally, line A'B' will have the same slope as line AB, but it will be located at the origin.
If line AB is dilated with a scale factor of 1/3, the effect would be the opposite. Line A'B' would be one-third the length of line AB, and it would still have the same slope as line AB. However, this time, line A'B' would be located closer to the origin.