Here are the solutions to the problems:
3.
The combined angle measure is 70∘. The two given angles are 45∘ and f∘.
Step 1: Set up the equation based on the sum of the angles.
45∘+f∘=70∘
Step 2: Solve for f.
f∘=70∘−45∘
f∘=25∘
The value of f is 25.
4.
The combined angle measure is 115∘. The two given angles are t∘ and 90∘ (indicated by the right angle symbol).
Step 1: Set up the equation based on the sum of the angles.
t∘+90∘=115∘
Step 2: Solve for t.
t∘=115∘−90∘
t∘=25∘
The value of t is 25.
5.
The combined angle measure is 180∘ (a straight angle). The two given angles are x∘ and 150∘.
Step 1: Set up the equation based on the sum of the angles.
x∘+150∘=180∘
Step 2: Solve for x.
x∘=180∘−150∘
x∘=30∘
The value of x is 30.
6.
The two given angles, 35∘ and r∘, form a right angle, which measures 90∘.
Step 1: Set up the equation based on the sum of the angles.
35∘+r∘=90∘
Step 2: Solve for r.
r∘=90∘−35∘
r∘=55∘
The value of r is 55.
7. Problem Solving
Step 1: Determine the angle between each number on a clock face.
A full circle is 360∘, and there are 12 numbers on a clock.
Angle per number = 12360∘=30∘.
Step 2: Identify the positions of the line and the minute hand.
The line is drawn to the number 12. The minute hand is on 2.
Step 3: Calculate the angle between the line at 12 and the minute hand at 2.
The minute hand moves 2 positions from 12 (from 12 to 1, and from 1 to 2).
Angle = 2×30∘=60∘.
The angle is 60∘.
8. Test Practice
The combined angle measure is 120∘. The two given angles are n∘ and 80∘.
Step 1: Set up the equation based on the sum of the angles.
n∘+80∘=120∘
Step 2: Solve for n.
n∘=120∘−80∘
n∘=40∘
The value of n is 40.
Comparing this to the given options:
A) 45
B) 40
C) 35
D) 30
The correct option is B).