Question

why shouldnt you tell a pigeon a secret? because it... write the letter of each answer in the box containing the matching number. name an angle with the given classification. 1. right angle 2. obtuse angle 3. straight angle 4. acute angle find the indicated angle measure given m∠bae = 59°. 5. m∠bac 6. m∠cad 7. m∠dae find the indicated angle measure given m∠bae = 130°. 8. m∠bac 9. m∠cad 10. m∠dae

Explanation:

Step1: Recall angle - type definitions

A right - angle measures 90°, an obtuse angle measures more than 90° but less than 180°, a straight angle measures 180°, and an acute angle measures less than 90°.

Step2: For questions 5 - 7

Given \(m\angle BAE = 59^{\circ}\), assume \(\angle BAE=\angle BAC+\angle CAD+\angle DAE\). Let \(\angle BAC=(4x - 20)^{\circ}\), \(\angle CAD=(x + 12)^{\circ}\), \(\angle DAE=(x + 1)^{\circ}\). Then \((4x - 20)+(x + 12)+(x + 1)=59\).
Combining like terms: \(4x+x+x-20 + 12+1 = 59\), \(6x-7 = 59\), \(6x=59 + 7=66\), \(x = 11\).
So \(m\angle BAC=4x-20=4\times11-20=44 - 20 = 24^{\circ}\), \(m\angle CAD=x + 12=11 + 12 = 23^{\circ}\), \(m\angle DAE=x + 1=11+1 = 12^{\circ}\).

Step3: For questions 8 - 10

Given \(m\angle BAE = 130^{\circ}\), assume \(\angle BAE=\angle BAC+\angle CAD+\angle DAE\). Let \(\angle BAC=(3x - 10)^{\circ}\), \(\angle CAD=(2x + 5)^{\circ}\), \(\angle DAE=(x + 15)^{\circ}\).
Combining like terms: \((3x-10)+(2x + 5)+(x + 15)=130\), \(3x+2x+x-10 + 5+15 = 130\), \(6x+10 = 130\), \(6x=130 - 10 = 120\), \(x = 20\).
So \(m\angle BAC=3x-10=3\times20-10=60 - 10 = 50^{\circ}\), \(m\angle CAD=2x + 5=2\times20+5=40 + 5 = 45^{\circ}\), \(m\angle DAE=x + 15=20+15 = 35^{\circ}\).

Answer:

1. No right - angle given in the options (assuming no \(90^{\circ}\) angle among the named angles).
2. No obtuse - angle given in the options (assuming no angle between \(90^{\circ}\) and \(180^{\circ}\) among the named angles).
3. No straight - angle given in the options (assuming no \(180^{\circ}\) angle among the named angles).
4. Acute angles could be many small - named angles.
5. R. \(24^{\circ}\)
6. C. \(12^{\circ}\)
7. P. \(11^{\circ}\)
8. R. \(50^{\circ}\)
9. I. \(45^{\circ}\)
10. S. \(35^{\circ}\)