In a quadrilateral , angle CAB is divided into two comgruent angles by line AD. What is the measure, in degrees of angle DAB. Angle B and D are 90 degrees. angle C equals 45 degrees.
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Suppose you intend to spend no more than $60 buying books. Hardback books cost $12 and paperbacks cost $5. How many books of each type can you buy?
90+45= 135
180-135= 45
To find the measure of angle DAB, we can use the fact that opposite angles of a quadrilateral are supplementary.
First, let's label the given angles in the quadrilateral:
Angle B = 90 degrees
Angle D = 90 degrees
Angle C = 45 degrees
Since angles B and D are right angles and angle C is less than 90 degrees, we know that angle A must be greater than 90 degrees.
Now, let's consider angle CAB. According to the given information, angle CAB is divided into two congruent angles by line AD.
Since angle A is greater than 90 degrees, the two congruent angles must each be less than 90 degrees.
Let's label each of the two congruent angles as x degrees.
Since angle CAB is divided into two congruent angles, we can represent the measure of angle CAB as 2x.
According to the property of a quadrilateral, opposite angles are supplementary. This means that angle CAB and angle BCD are supplementary. Since angle BC is a right angle (90 degrees), angle CAB is also 90 degrees.
Therefore, we can set up the following equation:
2x + 90 = 180
Simplifying the equation:
2x = 180 - 90
2x = 90
Dividing both sides of the equation by 2:
x = 45
So, each of the two congruent angles (angle DAB and angle DAC) measure 45 degrees.