Question

read the problem carefully and solve. show your work under each question.
keisha makes a map of the streets near her house. she uses angles and intersecting lines to represent the streets. she decides to label the lines and angles on her map. she also plans to measure some of the angles.
helpful hints
vertical angles are formed when two straight lines intersect. they are opposite angles and are equal.
two angles are supplementary if their sum is 180°.
two angles are complementary if their sum is 90°.
an angle bisector is a line drawn through the vertex of an angle that divides it into two angles that have the same measure.
use the figure below for questions 1 and 2.

1. keisha draws the pair of lines above to show the intersection of two streets. identify ∠d and ∠f as supplementary, complementary, or vertical.
2. in keisha’s drawing above, identify ∠f and ∠g as supplementary, complementary, or vertical.
3. keisha measures two complementary angles, ∠b and ∠c, on her map. the measure of ∠b is 35°. what is the measure of ∠c?
4. keisha measures two supplementary angles, ∠j and ∠k, on her map. the measure of ∠k is 124°. what is the measure of ∠j?
5. keisha draws ∠rst below. she draws ( overline{sv} ) so that it bisects ∠rst. the measure of ∠vst is 25°. what is the measure of ∠rst?

Explanation:

Step1: Identify ∠D and ∠F type

Vertical angles are opposite intersecting lines, equal. ∠D and ∠F are opposite, so vertical.

Step2: Identify ∠F and ∠G type

Supplementary angles sum to 180°. ∠F and ∠G form a straight line, so supplementary.

Step3: Calculate complementary ∠C

Complementary angles sum to 90°. $\angle C = 90^\circ - 35^\circ$

Step4: Calculate supplementary ∠J

Supplementary angles sum to 180°. $\angle J = 180^\circ - 124^\circ$

Step5: Calculate bisected ∠RST

Angle bisector splits angle into two equal parts. $\angle RST = 2 \times 25^\circ$

Answer:

1. Vertical
2. Supplementary
3. $55^\circ$
4. $56^\circ$
5. $50^\circ$